Physics

Problem

A simple pendulum consists of a bob of mass

m

suspended by a light, inextensible string of length

l

. For small angular displacements, the time-period of oscillation

T

is suspected to depend only on the length

l

, the mass

m

of the bob and the local acceleration due to gravity

g

. a. (i) Write the dimensional formulae of

T

l

m

and

g

. b. (ii) Assuming the functional form

T = k \, l^{\,a}\, m^{\,b}\, g^{\,c}

, where

k

is a dimensionless constant, determine the values of the exponents

a

b

and

c

by equating dimensions. c. (iii) Comment on whether the time-period of a simple pendulum depends on the mass of the bob, giving dimensional reasons for your answer.

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