A simple pendulum consists of a bob of mass suspended by a light
PHYSICS · Multi-part · CBSE · Physics · Units and Measurements · Units and Measurements
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.
(i) Write the dimensional formulae of T, l, m and g.
(ii) Assuming the functional form T=klambgc, where k is a dimensionless constant, determine the values of the exponents a, b and c by equating dimensions.
(iii) Comment on whether the time-period of a simple pendulum depends on the mass of the bob, giving dimensional reasons for your answer.