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Force ❖ Illustrative Examples 1) A 15 g bullet is fired from a gun of mass 2 kg with a speed of 1000 m/s. Find the recoil velocity of the gun. Data: m1 = 15g =15
10-3kg, m2 = 2kg V1 = 1000m/s, v2 =?
(Ans: -7.5m/s)
2) A3 kg ball and 4 kg ball having speed 7 m/s and 5 m/s approach one another. Find their speeds after collision if the coefficient of restitution is 0.75. Data: m2 = 3 kg, m2 = 4 kg, U1 = 7 m/s, u2 = -5 m/s, e = 0.75, Vl =? v2 =? (Ans: 4 m/s) 3) A graduated uniform metre rod is balanced horizontally on a knife edge at a distance of 10 cm from its centre of gravity, when masses of 50 g and 30 g are suspended at the 5 cm and 90 cm divisions of the rod. Find the weight of the rod. Data: m1 = 50 g , m2 = 30 g, d1 = 35 cm, d2 = 50 cm w = ?
(Ans: 25gwt)
4) Two brass spheres of radii 5 cm and 10 cm are brought in contact with each other. Find the centre of gravity of the combination. Data: r1 = 5 cm, r2 = 10 cm
(Ans:
)
5) Find the position vector of the centre of mass of 1 kg, 2 kg and 3 kg at points and
respectively.
Data: m1= 1kg, m2 = 2kg, m3 = 3kg
(Ans: 6) A force is given by
)
N acts on a body at a point whose distance from the axis of rotation Determine the magnitude and direction of the torque acting on
the body.
(Ans: Positive)
7) A uniform ladder of length 10m and weight 100 kg is kept with its lower end on a smooth horizontal floor and the upper end on a smooth vertical wall. A horizontal string tied to the bottom of the ladder keeps it in equilibrium. Find the tension along the string if a man weighing 60 kg goes up by 3 m in the ladder which is inclined at 30° with the horizontal. Data: w = 100 kg wt, = 30°, AB =
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w, = 60kgwt, = 10m T = ?
(Ans:
) Force
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8) A man weighing 50 kg is standing in a lift. Find the thrust (apparant weight) on a floor of the lift when i) lift ascends with an acceleration of 5m/s2 (Take g = 10m/s2) ii) lift descends with an acceleration of 5 m/s2. iii) lift is ascending, with uniform velocity 3m/s
(Ans: 750 N, 250N and 50N)
9) A block of mass m1 = 3.7 kg on frictionless inclined plane of angle 30° is connected to a string over a massless, frictionless pulley to a second block of mass m2 = 2.3 kg hanging vertically. What is (A) the magnitude of acceleration of each block (B) the direction of acceleration of the hanging block? (C) the tension in the string? (g = 9.8 m/s2) Data: m1 = 3.7 kg,
= 30°, m2 = 2.3 kg.
(Ans: a) a = 0.735 m/s2, b) As m2g > m1gsin
, the mass ‘m2’ will move in downward
direction with an acceleration ‘a’. c) T = 20.85N) 10) A cyclist moves on a road stops due skidding covering 10 m. During this process, the net force on the cycle due to road is 100 N and opposite to the motion. How much work is done by the road on the cycle and vice-versa? (Ans: w = -1000 J. Work done by cycle on road and vice versa are not equal) 11) A drop of liquid of mass 2g falling from height 2km. It hits the ground with speed 25 m/s. What is the work done by (i) the gravitational force? (ii) the unknown force? (g = 10m/s2) Data: m = 2
10-3 kg, v = 25 m/s h = 2
103 m.(Ans:
, wg = -39.375J)
12) A block of mass 1kg moving on a horizontal surface with speed 4m/s enters a rough patch ranging from x = 0.1 m to x = 2.2 m. The retarding force (f) on the block in its range is inversely proportional to x over this range.
Where k = 0.5 What is the final kinetic energy and speed of the block as it crosses this patch? Data: m = 1 kg, u = 4 m/s
(Ans: (K.E)final = 7.3288 J and VF = 3.828 m/s)
13) A flexible chain of length L and mass M is slowly pulled at constant speed up over the edge of a table by a force f parallel to the edge of the table. Assume that there is no friction-between the table and the chain, calculate the work done. (Ans:
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)
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� Theory Question 1) What do you mean by real farce and psuedo force? 2) State and derive law of conservation of linear momentum in case of a colliding bodies 3) In head on collision of two bodies, derive the expressions for the velocities of the bodies in terms of their masses and velocities before collision. 4) Distinguish between elastic and inelastic collision. Give examples 5) Define the coefficient of restitution between two colliding bodies and state its value for perfectly elastic and inelastic collision. 6) Explain the terms: inertial frame of reference and non-inertial frame of reference. 7) Explain the concept of pseudo force in non-inertial frame of reference. 8) Define the term moment of force about a point. State its SI unit and dimensions and write the vector form. 9) What do you mean by couple? State and explain its properties. 10) Define the terms centre of mass and centre of gravity of a body. Under what conditions the centre of gravity and centre of mass coincide? 11) State the conditions of equilibrium of a body under the action of a number of coplanar forces. 12) Explain the concept of work done by a variable force. 13) State and explain work energy theorem. 14) Define force and state its units and dimensions. 15) State Newton's first law of motion. How is it related with inertia of a body? 16) An astronaut accidentally gets separated out of his small spaceship accelerating in inter stellar space at a constant rate of 100 m s-2. What is the acceleration of the astronaut the instant after he is outside the spaceship? (Assume that there are no nearby stars to exert gravitational force on him.) 17) State and explain Newton’s second law of motion. 18) Explain why a cricketer moves his hands - backwards while holding a catch. 19) State and explain Newton's third law of motion. 20) Give the magnitude and direction of the net force acting on: I. II.
a drop of rain falling down with a constant speed. a cork of mass 10 g floating on water.
III.
a kite skillfully held stationary in the sky.
IV.
a car moving with a constant velocity of 30 kmh-1 on a rough road.
V.
a high speed electron in space far from all gravitating objects, and free of electric and magnetic fields.
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21) Explain the concept of impulse. Write down its unit and dimension. 22) If a body is not accelerated, does a force act on it or not? 23) Large force always produces large change in momentum on a body than a small force. Is this correct? 24) Name the different types of fundamental forces in nature. 25) Define gravitational force. Give its examples. 26) State Newton's law of gravitation. 27) Write down the main characteristics of gravitational force. 28) Define electrostatic force and magnetic force. 29) Write a note on electromagnetic force. 30) State characteristics of electromagnetic force. 31) Write a note on nuclear force. 32) Discuss the characteristics of strong nuclear forces. 33) Discuss the characteristics of weak nuclear forces. 34) Define the following terms. (i) Conservative force (ii) Non-conservative force. 35) Define momentum. Discuss its unit and dimension. 36) Give 2 examples of principle of conservation of linear momentum. 37) Explain recoiling of the gun on the basis of conservation of momentum and obtain an expression of the recoil velocity of gun in terms of muzzle velocity of the bullet. OR Explain the principle of conservation of linear momentum, with an example. 38) Explain the principle of conservation of linear momentum in rocket propulsion. (Motion). 39) Explain how linear momentum is conserved during the explosion of a bomb. 40) Explain graphically the work done by a variable force. 41) Work and kinetic energy are equivalent quantities, justify. 42) When ball rolls down an inclined plane, its momentum increases. Is the momentum conserved? 43) The sign of work done by a force on a body is important to understand. State carefully if the following quantities are positive or negative: I.
Work done by a man in lifting a bucket out of a well by means of a rope tied to the bucket.
II. III.
Work done by gravitational force in the above case. Work done by friction on a body sliding down an inclined plane.
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Work done by an applied force on a body moving on a rough horizontal plane with uniform velocity.
V.
Work done by the resistive force of air on a vibrating pendulum in bringing it to rest.
44) Explain elastic collision with examples. 45) Explain inelastic collision with two examples. 46) Define perfectly inelastic collision. 47) Two particles undergo one-dimensional, head-on, perfectly inelastic collision. Derive an expression for their final velocity in terms of their masses and initial velocities. 48) Explain elastic collision in two dimensions. 49) Define the term frame of reference. Give example and its importance. 50) Distinguish between inertial frame of reference and non-inertial frame of reference. 51) Explain existence of pseudo force in a. a lift b. a car c. a moving bus 52) Define the following terms.
i. Rigid body
ii. Axis of rotation
53) Define moment arm. 54) Prove that in rotational motion of a rigid body,
. Also discuss its direction of
rotation. 55) Show that moment of couple about any point in its plane is always constant and equal to the product of magnitude of one of the forces and perpendicular distance between them.
OR
Show that moment of a couple does not depend on the point about which you take the moments. 56) Explain the concept of centre of mass using suitable example. 57) Give the location of the centre of mass of a (i) sphere, (ii) cylinder. (iii) ring, and (iv) cube, each of uniform mass density. Does the centre of mass of a body necessarily lie inside the body? 58) A child sits stationary at one end of a long trolley moving uniformly with a speed V on a smooth horizontal floor. If the child gets up and runs about on the trolley in any manner, what is the speed of the CM of the (trolley + child) system? 59) Derive an expression for the position of centre of mass of a system of two particles: How can the treatment be extended for n masses? 60) Explain the concept of centre of gravity.
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61) Explain the method to determine centre of gravity of irregular bodies. 62) Explain with an example, for very large bodies, the centre of gravity does not coincide with the centre of mass. 63) In the ship or boat, heavy load is kept at the bottom. Explain why.
â?– Textbook Problems 1) A bullet of mass 0.1 kg moving horizontally with a velocity of 20 m/s strikes a target and brought to rest in 0.1 s. Find the impulse and average force of impact. (Ans: 2 N-s , 20N). 2) A ball whose mass is 100 g is dropped from a height of 2 m from tire floor. It rebounds vertically upwards after colliding with tire floor to a height 1.5 m. Find (a) the momentum of the ball before and after colliding with the floor (b) the average force exerted by the floor on the ball. Assume that collision lasts for 10-8 s. (Ans: +0.626kg m/s , -0.542m/s , 1.168
)
3) A metal ball falls from a height 1 m onto a steel plate and jumps up to a height of 0.81 m. Find the coefficient of restitution.
(Ans: 0.9)
4) Two masses undergo a perfectly elastic head-on Collision. The first mass 'm' moves with initial velocity of 50 m/s in the + ve x direction. The second mass '2m' moves with initial velocity of 40 m/s in the -ve x direction. i) Calculate their final velocities, ii) What is the ratio of the final K.E. to the initial K.E. for mass 'm? iii) Calculate the change in momentum of masses m and 2m if m = 1kg. What is the change in momentum of the system? (Ans: -70m/s, 20m/s, 1.96,-120m/s and 120m/s) 5) A bar of 2.0 m long makes an angle of 300 with the horizontal. A vertical force of 40 N is applied 0.4 m from the upper end. Calculate the torque due to this force about each end.
(Ans: 55.4Nm 13.856Nm)
6) The mass of moon is 0.0123 times the mass of the earth and seperation between them is 3.84 the earth.
. Determine the location of C.M as measured from the centre of (Ans: 4.67
)
7) A uniform wooden plank 5 m long and weighing 40 kg is resting on two supports 0.5 m from each end. A boy weighing 45 kg stands 1.5 m from one end of the wooden plank. Find the reactions at the supports. (Ans: R1 = 53.75 kg wt R2 = 31.25 kg wt) 8) A 15 m ladder weighing 50 kg rests against a smooth wall at a point 12 m above the ground. The centre of gravity, of the ladder is one third the way up. A 80 kg man
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climbs half way up the ladder. Find the forces exerted by the system on the ground and the wall.
(Ans: 136.8 kgwt, 42.5 kgwt)
9) Locate the centre of mass of three particles of mass m1 = 1 kg, m2 = 2 kg and m3 = 3 kg at the corners of an equilateral triangle of each side of 1 m. (Ans:
)
10) Two masses m1 & m2 are connected to the two ends of a massless string passing over a frictionless massless pulley and m2 is placed on an inclined plane. Assume the friction between the mass m2 and the plane is zero. Find the acceleration of the masses and the tension in the string if m1 = 20.5kg, m2 = 10.5kg and
.
(Ans: 4.13m/s2, 116.23N) 11) Two bodies of masses 2 kg and 4 kg are connected to the ends of a string of negligible mass and then passed around a frictionless pulley. Calculate (i) the acceleration of the system and (ii) the tension in the string. (Take g = 10m/s2) (Ans: Take g = 10m/s2) 12) A person weighs 60 kg. He stands on a weighing machine in a lift, which is moving (i) upwards with uniform speed 5m/s (ii) downwords with uniform acceleration of 4m/s2 (iii) upwards with a uniform acceleration of 4m/s2. What would be the reading on the scale in each case? (Take g = 10m/s2) (Ans: (i) 600N (ii) 360N (iii) 840N) 13) A man trying to lose weight lifts a 10 kg mass one thousand times to a height of 0.5m each time. Assume that the potential energy lost each time, he lowers the mass is dissipated. What is the work does he do against the gratational force? Fat supplies 3.8
107 J of energy per kilogram which is converted to mechanical
energy with a 2O% efficiency rate. How much fat will the man use up? (Ans: (i)
(ii)
)
14) A particle of mass 12 kg is acted upon by a force f = (100 - 2 x2) where f is in newton and 'x' is in metre. Calculate the work done by this force in moving the particle x = 0 to x = -10 m. What will be the speed at x = 10 m if it starts from rest? (Ans: W = 33 J, V = 7.46m/s) 15) A position dependent force f = 7 - 2x + 3x2 newton acts on a small body of mass 2 kg and displaces from x = 0 to x = 5. Calculate the work done.
(Ans: 135 J)
16) A liquid drop of 1.00 g falls from a height of a cliff 1.00 km. It hits the ground with a speed of 50 ms-l. What is the work done by the unknown resistive force. (Ans: -8.75 J)
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17) A bullet of mass 0.012 kg and horizontal speed 70 ms-1 strikes a block of wood of mass 0.4 kg and instantly comes to rest with respect to the block. The block is suspended from the ceiling by means of thin wires. Calculate the height to which the block rises and also estimate the amount of heat produced in the block. (Ans: h = 21.2 cm, w = 28.5 J))
� Practice Problems ➢ Type-I : Problems based on force and impulse 1) If a constant force of 800 N produces an acceleration of 5 m/s2 in a body, what is its mass? If the body starts from rest, how much distance will it travel in 10 s? (Ans: 160 kg, 250m) 2) Two billiard balls each of mass 0.05 kg moving in opposite directions with speed 6 m s-l collide and rebound with the same speed. What is the impulse imparted to each ball due to the other?
(Ans: -0.6 kgms-1)
3) A batsman deflects a ball by an angle of 450 without changing its initial speed which is equal to 54 km/h. What is the impulse imparted to the ball? (Mass of the ball is 0.15 kg.)
(Ans: 4.157 kgms-1)
4) A cricket ball of mass 150 g moving with a velocity of 12 m/s is turned back with a velocity of 20 m/s on hitting the bat. The force of the ball lasts for 0.01 s. Find the average force exerted on the ball by the bat.
(Ans: 480N)
5) A 20 g bullet leaves a machine gun with a velocity of 200 m/s. If the mass of the gun is 20kgo find its recoil velocity. If the gun fires 20 bullets per second, what force is to be applied to the gun to prevent recoil?
(Ans: 0.2 m/s, 80N)
6) A constant force acting on a body of mass 3 kg changes its speed from 2 m s-1 to 3.5 m/s in 25 s. The direction of motion of the body remains unchanged. What is the magnitude and direction of the force?
(Ans: 0.18N)
7) A constant retarding force of 50 N is applied to a body of mass 20 kg moving initially with a speed of 15m s-1. How long does the body take to stop?
(Ans: 6 s)
8) A constant force acts on a body of mass 100 g for 4 s. The body starting from rest covers a distance of 0.64 m during this time. Find the force.
(Ans:
)
9) An engine of mass 60 metric tons has a velocity of 72 km/h. What force will stop it within a distance of 100 m? What force will stop it in 20 s? (Ans:
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10) What constant force is needed to increase the momentum of a body from 2300 kg m/s to 3000 kg m/s in 50 s?
(Ans: 14 N)
11) A bullet leaves the rifle of mass one kg and the rifle recoils thereby with a velocity of 30 cm/s. If the mass of bullet is 3 g find the velocity of the bullet.
(Ans: 100 m/s)
12) A machine gun fires 180 bullets per minute on a steel plate. Each bullet has a mass of 20 g and velocity 1 km/s. The bullets return with half their velocity after hitting the plate. Find the force necessary to hold the plate so as not to move it. (Ans: 90 N) 13) While launching a rocket of mass 2
104 kg, a force of 5
105 N is applied for 20 s.
Calculate the velocity attained by the rocket at the end of 20 s.
(Ans: 500 m s-1)
14) A bullet weighing 10 g is fired with a velocity of 800 m s-1. After passing through mud wall 1 m thick, its velocity decreases to 100 m s-1. Find the average force of resistance offered by the mud wall?
(Ans: 3150 N)
➢ Type-II : Problems based on work and energy 15) A body of mass 0.5 kg travels in a straight line with velocity v = ax3/2 where a = 5 m1/2
s-1. What is the work done by the net force during its displacement from x = 0 to
x = 2 m?
(Ans: 50 J)
16) A body constrained to move along the z-axis of a coordinate system is subject to a constant force F given by
N where , ,
are unit vectors along the x,
y, and z axis of the system respectively. What is the work done by this force in moving the body a distance of 4 m along the z-axis?
(Ans: 12 J)
17) A bullet of mass 25 g was moving at the rate of 500 m s-1. After passing through a solid substance, it continued to move at the rate of 100 m s-1. How much work the bullet had to do in passing through the substance?
(Ans: 3000 J)
➢ Type-III : Problems based on head-on collision 18) A shell of mass 0.020 kg is fired by a gun of mass 100 kg. If the muzzle speed of the shell is 80 m s-1, what is the recoil speed of the gun?
(Ans: 0.016 ms-1)
19) A 10 kg maps moving at 5 m/s collides head-on with a 4kg mass moving at 2 m/s in the same direction. If e = , find their velocity after impact.
(Ans:
)
20) Two bodies of masses 5 kg and 3 kg moving in the same direction along the same straight line with velocities 5 m s-1 and 3 m s-1 respectively suffer one-dimensional elastic collision. Find their velocities after the collision.
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(Ans: 3.5 m/s, 5.5 m/s)
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21) A body of mass 1 kg and velocity 10 m/s collides with another body of mass 3 kg and velocity 2 m/s coming from the exactly opposite direction. If on collision the bodies merge into one, find the magnitude and direction of their common velocity. (Ans: 1 m/s in the direction of former) 22) A body of mass 100 kg moving with a velocity of 50 m/s strikes another body of mass 200 kg which is at rest. If the two bodies after collision stick together, then calculate the velocity of the composite body.
(Ans: 16.67 m/sec)
23) A sphere of mass 2 kg travelling with a velocity of 22 m/s makes a head – on collision with a sphere of mass 4 kg travelling with a velocity of 10 m/s in the same direction. If the coefficient of restitution is 0.8, find the velocities of the two spheres after collision.
(Ans: 7.6m/s, 17.2 m/s)
➢ Type-IV : Problems based on moment of force (Torque) 24) A force
is applied at a point (3, 4, -2). Find its torque about the point
(-1, 2, 4).
(Ans:
)
25) Two weights 5 kg and 8 kg are suspended from a uniform rod of length 10 m and weighing 3 kg. The distances of the weights from one end are 2 m and 7 m. Find the point at which the rod balances.
(Ans: 5.1 m)
26) A metre stick is balanced on a knife edge at its centre. When two coins, each of mass 5 g are put one on top of the other at the 12.0 cm mark, the stick is found to be balanced at 45.0 cm. What is the mass of the metre stick?
(Ans: 66 g)
27) A uniform rod balances about a point 2 m from one end when a weight of 0.18 kg is suspended from that end. It also balances about a point 3 m from the same end when a weight of 0.08 kg is suspended from the same end. Find the length and weight of the rod.
(Ans: 10 m, 0.12 kg)
28) A uniform rod of length 6 m and weight 200 gwt. is suspended horizontally by two cords of equal lengths tied to it at distances 1.6 m and 2.4 m respectively from the mid-point. Find the tension in each cord.
(Ans: 120 gwt, 80gwt)
29) A uniform rod AB is resting on two supports which are at distances 3 m and 4 m from the ends A and B respectively. Masses of 10 kg and 8 kg are suspended from the ends A and B respectively. The weight of the rod is 45 kg and its length is 12 m. Find the reaction at the supports.
(Ans: 27.6 kg wt, 35.4 kg wt)
30) A uniform ladder 5 m long and weighing 20 kg leans against a vertical frictionless wall with its lower end 4 m away from the foot of the wall. Find the magnitudes of the forces exerted on the ladder at each of the ends.
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(Ans: 13.3 kg wt, 24 kg wt)
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➢ Type-V : Problems based on centre of mass and centre of gravity 31) Three particles of masses 3 g, 5 g and 8 g are situated at point (2,2,2) (-3, 1, 4) and (-1,3, -2) respectively. Find the position vector of their centre of mass. (Ans:
)
32) In the HC molecule, the separation between the nuclei of the two atoms is about 1.27
(1
: 10-10m). Find the approximate location of the CM of the molecule,
given that a chlorine atom is about 35.5 times as massive as a hydrogen atom and nearly all the mass of an atom is concentrated in its nucleus.
(Ans: 1.235
)
33) Three equal masses each of 1kg are placed on vertices of an equilateral triangle whose each side is lm long. Find the position of the centre of mass. (Ans: x = 0.5m, y = 0.29m) 34) Locate the centre of mass of a system of two uniform spherical masses of 5 kg and 35 kg, kept with their centres 70 cm apart. (Ans: 0.6125 m from centre of 5 kg mass)
➢ Type-VI : Miscellaneous 35) A bullet of mass 10 gram strikes a target with a velocity of 100 m s-1 and comes to rest after piercing 5 cm into it. Calculate the average force of resistance offered by the target.
(Ans: 1000 N)
36) A ball of mass 0.2 kg moving with a velocity of 2 m/s on a plane surface collides with another ball of the same mass and initially at rest. If the coefficient of restitution between the two bails is 0.6, find the velocities of the two balls after collision.
(Ans: 0.4 m/s, 1.6 m/s)
37) A constant retarding force of 50 N is applied to a body of mass 20 kg moving initially with a speed of 15 m s
-1.
How long does the body take to stop?
(Ans: 6 s)
38) A 30 g bullet leaves a rifle with a velocity of 300 m s-1 and the rifle recoils with a velocity of 0.60 m s-1. Find the mass of the rifle.
(Ans: 15 kg)
39) An elevator weighs 4000 kg. When the upward tension in the supporting cable is 48000 N, what is the upward acceleration? Starting from rest, how far does it rise in 3 s?
(Ans: 2.2 m s-2, 9.9 m)
40) Point masses of I kg, 2 kg,3 kg and 4 kg are placed at the corners A, B, C and D respectively of a square whose each side is 1 m long. Find the position of the centre of mass of the system.
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(Ans: 0.7 m, 0.5 m)
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41) A constant force acts on a body for 3 seconds and then ceases to act. During next 5 seconds the body describes 75 m. If the mass of the body is 8 kg, find the magnitude of the force.
(Ans: 40 N)
42) Four particles of masses 2 kg, 3 kg, 4 kg and 5 kg are placed at the corners of a square of length 2 m of each side. Find the co-ordinates and position vector of its centre of mass.
(Ans:
)
43) Two masses 7 kg and 12 kg are connected at the two ends of a light inextensible string that passes over a frictionless pulley. Find the acceleration of the masses and the tension in the string, when the masses are released.
(Ans: 2.58 ms-2, 86.66 N)
44) A block of mass 0.8 kg is dragged along a level surface at constant velocity by a hanging block of mass 0.2 kg. Calculate the tension in the string and the acceleration of the system.
(Ans: 1.568 N, 1.96 m s-2)
45) A man weighs 70 kg, He stands on a weighing machine in a lift, which is moving a. upwards with uniform speed of 10 m s-l b. downwards with a uniform acceleration of 5 m s-2 C. upwards with uniform acceleration of 5 m s-2. What is the reading on the scale in each case?
(Ans: 686 N, 336 N, 1036 N)
46) A bolt of mass 0.3 kg falls from the ceiling of an elevator moving down with a uniform speed of 7 m s-1. It hits the floor of the elevator which is 3 m below and does not rebound. How much is the heat energy produced? 47) A force
(Ans: 8.82 J)
N acts on a particle, whose position with respect to the origin 'O' of
an inertial reference frame is given by,
m. Determine the torque acting on
the particle.
(Ans: 5 Nm, Positive z – axis)
48) Two weights 4 kg and 6 kg are suspended from a uniform rod AB of length 10 m and weighing 2 kg. The distances of the weights from one end are 2.5 m and 7.5 m. Find the point at which the rod balances.
(Ans: 5.4 m from A)
â?– Multiple Choice Questions 1) A body of mass 2 kg moving on a horizontal surface with initial velocity of 4 m s-1 comes to rest after two seconds. If one wants to keep this body moving on the same surface with a velocity of 4 m s-1, the force required is (A) 2N
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(B) 4N
(C) 0
(D) 8N
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2) What force will change the velocity of a body of mass 1 kg from 20 m s
-1
to 30 m s-1
in two seconds? (A) 1N
(B) 5N
(C) 10 N
(D) 25 N
3) A machine gun has a mass 5 kg. It fires 50 gram bullets at the rate of 30 bullets per minute at a speed of 400 ms-1. What force is required to keep the gun in position? (A) 10 N
(B) 5N
(C) 15 N
(D) 30 N
4) A force of 5 newton acts on a body of weight 9.80 newton. What is the acceleration produced in metre per sec2? (A) 0.51
(B) 1.96
(C) 5.00
(D) 49.00
5) A body of mass m strikes a wall with velocity v and rebounds with the same speed. Its change in momentum is (A) 2 mv
(B) mv/2
(C) -mv
(D) Zero
6) A ball of mass 0.2 kg is dropped from a certain height above the ground. It bounces back after an elastic collision with the floor. If the speed with which the ball strikes the ground is 10 m/s, then the impulse imparted by the ball on the floor is (A) 120 kg m/s
(B) 8 kg m/s
(C) 4 kg m/s
(D) 2 kg m/s
7) A force of 6 N acts on a body of mass 1 kg initially at rest and during this time, the body attains a velocity of 30 m/s. The time for which the force acts on a body is (A) 10 second
(B) 8 second
(C) 7 second
(D) 5 second
8) A bullet of mass 10 g is fired from a gun of mass 1 kg with recoil velocity of gun = 5 m/s. The muzzle velocity will be (A) 30 km/min
(B) 60 km/min
(C) 30 m/s
(D) 500 m/s
9) The velocity of rocket with respect to ground is v1 and velocity of gases ejecting from rocket with respect to ground is v2. Then velocity of gases with respect to rocket is given by (A) v2
(B) v1 + v2
(C) v1 x v2
(D) v1
10) A rocket of initial mass 6000 kg ejects gases at a constant rate of 16 kg/s with constant relative speed of 11 km/s. What is the acceleration of rocket one minute after the blast? (A) 25 m/s2
(B) 50 m/s2
(C) 10 m/s2
(D) 35 m/s2
11) Two bodies A and B of masses 1 kg and 2 kg moving towards each other with velocities 4 m/s and 1 m/s suffers a head on collision and stick together. The combined mass will (A) move in direction of motion of lighter mass. (B) move in direction of motion of heavier mass. (C) not move.
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(D) move in direction perpendicular to the line of motion of two bodies. 12) A machine gun fires a bullet of mass 40 gram with velocity 1200 m/s. The man holding it can exert a maximum force of 144 N on the gun. How many bullets can he fire per second at the most? (A) only one
(C) any number of bullets
(B) 3
(D) 144
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13) Which of the following has maximum momentum? (A) A 100 kg vehicle moving at 0.02 m s-1. (B) A 4 g weight moving at 1000 cm s-1. (C) A 200 g weight moving with kinetic energy of 10-6 J. (D) A 200 g weight after falling through one kilometre. 14) A bullet hits and gets embedded in a solid block resting on a horizontal frictionless table. What is conserved? (A) Momentum alone.
(C) Momentum and K.E. both.
(B) KE alone.
(D) P.E. alone.
15) The force exerted by the floor of an elevator on the foot of a person standing there, is more than his weight, if the elevator is (A) going down and slowing down.
(C) going up and slowing down.
(B) going up and speeding up.
(D) either (A) and (B).
16) If E, G and N represents the magnitudes of electromagnetic, gravitational and nuclear forces between two electrons at a given separation, then, (A) N = E = G
(C) N > G < E
(B) E < N < G
(D) E > G > N
17) A body subjected to three concurrent forces is found to be in equilibrium. The resultant of any two forces (A) is equal to third force.
(C) is collinear with the third force.
(B) is opposite to third force.
(D) all of the above statements are true.
18) For an inelastic collision, the value of e is (A) greater than 1 (B) less than 1
(C) equal to 1
(D) none of these
(C) e = 1
(D) none of these
19) For a perfect elastic collision (A) e > 1
(B) e < 1
20) A perfect inelastic body collides head on with a wall with velocity v. The change in momentum is (A) mv
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(B) 2mv
(C) zero
(D) none of these.
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21) Two masses ma and mb moving with velocities va and Vb in opposite direction collide elastically and after the collision ma and mb move with velocities Vb and va respectively. Then the ratio mamb is (A)
(B)
(C) 1
(D)
22) The frictional force acts ________. (A) in direction of motion (B) against the direction of motion (C) perpendicular to the direction of motion (D) at any angle to the direction of motion 23) A marble of mass X collides with a block of mass Z, with a velocity Y, and sticks to it. The final velocity of the system is (A)
(B)
(C)
(D)
24) Two balls lying on the same plane collide. Which of the following will be always conserved ? (A) heat
(C) kinetic energy
(B) velocity
(D) linear momentum.
25) A body is moving with uniform velocity of 50 km h-1, the force required to keep the body in motion in SI unit is (A) zero
(B) 10
(C) 25
(D) 50
26) A coolie holding a suitcase on his head of 20 kg and travels on a platform, then work done in joule by the coolie is (A) 198
(B) 98
(C) 49
(D) zero
27) Out of the following forces, which force is non-conservative? (A) gravitational
(B) electrostatic
(C) frictional
(D) magnetic
28) The work done in conservative force is __________. (A) negative
(B) zero
(C) positive
(D) infinite
29) The angle between the line of action of force and displacement when no work done (in degree) is (A) zero
(B) 45
(C) 90
(D) 120
30) If the momentum of a body is doubled, its K.E. increases by (A) 50%
(B) 300%.
(C) 100%
(D) 400%
31) In perfectly inelastic collision, which is conserved? (A) P.E. only
(C) momentum only
(B) K.E. only
(D) K.E. and momentum
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32) A man pushes a wall and fails to displace it, he does _______. (A) negative work
(C)positive work but not maximum work
(B) no work at all
(D) maximum positive work
33) K.E. of a body is __________. (A) negative
(C) can be positive, zero
(B) positive
(D) infinite
34) In case of elastic collision, which is true? (A) Momentum and K.E. is conserved. (B) Momentum conserved and K.E. not conserved. (C) Momentum not conserved and K.E. conserved. (D) Momentum and K.E. both not conserved. 35) Pseudo force is true only in (A) frame of reference which is at rest. (B) inertial frame of reference. (C) frame of reference moving with constant velocity. (D) non-inertial frame of reference. 36) A man weighing 80 kg carries a stone of 20 kg to the top of the building 30 m high. The work done by him is (g = 9.8 m/s2) (A) 80 J
(B) 100 J
(C) 980 J
(D) 29,400 J
37) A weight lifter is holding a weight of 100 kg on his shoulders for 45 s, the amount of work done by him in joules is (A) 4500
(B) 100
(C) 45
(D) zero
38) A work performed on an object does NOT depend upon (A) force applied.
(C) initial velocity of the object.
(B) angle at which force is inclined.
(D) displacement.
39) If m is the mass of a body and E its K.E., then its linear momentum is (A)
(B)
(C)
(D)
â?&#x2013; Answer to Multiple Choice Question 1. (D)
2. (B)
3. (A)
4. (C)
5. (A)
6. (D)
7. (D)
8. (D)
9. (B)
10. (D)
11. (A)
12. (B)
13. (D)
14. (A)
15. (D)
16. (D)
17. (D)
18. (B)
19. (C)
20. (A)
21. (C)
22. (B)
23. (B)
24. (D)
25. (A)
26. (D)
27. (C)
28. (B)
29. (C)
30. (B)
31. (C)
32. (B)
33. (C)
34. (A)
35. (D)
36. (D)
37. (D)
38. (C)
39. (D)
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