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Measurements
❖ Illustrative Examples 1) Force experienced by charge ‘q’ moving with velocity ‘v’ in a magnetic field ‘B’ is given by F = qvB. Find the dimensions of magnetic field.
(Ans.
)
2) Find the conversion factor between S.I. unit and CGS unit of density. (Ans.
)
3) Check whether the equation is dimensionally correct, (Ans.
)
Each term does not have the same dimensions hence the equation is dimensionally incorrect. 4) The frequency (n) of vibration of a wire under tension depends upon the tension (T), mass per unit length (m) and vibrating length
of the wire. Using dimensional
analysis, obtain the dependence of frequency on these quantities.(Ans. 5) The radius of a nucleus of mass number ‘A’ is given by
) Find the
order of magnitude of radius for a nucleus with ( Ans.
Order of magnitude is
m.)
6) The length of a metal plate was measured using a vernier callipers of least count 0.01 cm. The measurements made were 3.11 cm, 3.13 cm, 3.14 cm and 3.14 cm. Find the mean length, the mean absolute error and the percentage error in the measurement of length. Data :
( Ans.
)
7) Find the percentage error in kinetic energy of a body of mass moving with a velocity of
cm/s.
and (Ans.
)
Data :
❖ Theory Questions F.Y.J.C. Science
Measurements