PHYSICS GRAVITATION PHYSICS : SHEET
GRAVITATION
SHEET LAWS OF MOTION
NEWTON’S LAW OF GRAVITATION Newton in 1687 proposed force law that we call Newton’s law of gravitation. According to him, “every particle of matter in the universe attracts every other particle with a gravitational force whose magnitude is directly proportional to the product of the masses of the particls and inversely proportional to the square of the distance between them”. Thus, m1m 2 r2 Here, m1 and m2 are the masses of the particles, r is the distance between them and G is the gravitational constant, with a value that is now known to be FG
G = 6.67 × 10–11 N–m2/kg2 G = 6.67 × 10–11 m3/kg–s2
1. 2. 3.
The direction of the force F is along the line joining the two particles. Regarding gravitational force, following points should be noted : The gravitational force between two particles is independent of the presence of other bodies or the properties of the intervening medium. Gravitational force is conservative force, therefore work done in displacing a body from one place to another is independent of path. It depends only on initial and final positions. The gravitational force obeys Newton’s third law i.e., F12 F21
C1 : Calculate the gravitational force of atraction between two spherical bodies, each of mass 1000 kg if the distance between their centre is 10 metre. (G = 6.67 × 10–11 Nm2 kg–2) Sol.
FG
m1m2 1000 1000 6.67 1011 2 r (10)2
F = 6.67 × 10–7 newton. Vector form of the law Let us denote by F12 the force on m1 by m2. Similarly F21 denotes the force on m2 by m1. Then F12 F 21 .
A m1 A
r12
F12 r1
F21
B
B That is, Newton’s law of gravitation obeys. Newton’s third law of motion m2 r2 (in strong form). The force on m1 is directed towards m2 and that on m2 is O directed towards m1. It is a central force. Let be r12 be position vector of m1 with respect to m2. From vector addition law, we get, r12 r 2 r1 r12 r1 r 2 Now F12 can be written as the product of magnitude and direction (unit vector). The direction of F12 is r12 opposite to r12 . Hence s the unit vector in the direction of F12 . | r12 |
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