A simple pendulum of length performs small‐amplitude oscillations so that its time…

PHYSICS · Multi-part · CBSE · Physics · Units and Measurements · Units and Measurements

Problem

A simple pendulum of length

l

performs small‐amplitude oscillations so that its time period is given by the relation

T = 2\pi\sqrt{\dfrac{l}{g}}

where

g

is the acceleration due to gravity. (i) Write the dimensional formulas of (a) length

l

and (b) acceleration due to gravity

g

. (ii) Using dimensional analysis, show that the above expression for

T

is dimensionally consistent. (iii) A student proposes an alternative relation

T = 2\pi\sqrt{\dfrac{g}{l}}

. Use dimensional reasoning to justify why this expression cannot be correct.