Identify the correct statement.

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) The time period of a simple pendulum is given by $T = 2\pi \sqrt{\frac{\ell}{g}}$.When temperature changes,the length changes as $\ell = \ell_0(1

Vedclass · Accepted Answer

The fractional change in the time period of a pendulum on changing the temperature is independent of the length of the pendulum.

Vedclass · Answer

(D) The time period of a simple pendulum is given by $T = 2\pi \sqrt{\frac{\ell}{g}}$.When temperature changes,the length changes as $\ell = \ell_0(1 + \alpha \Delta 	heta)$.The time period becomes $T' = 2\pi \sqrt{\frac{\ell_0(1 + \alpha \Delta 	heta)}{g}} = T(1 + \alpha \Delta 	heta)^{1/2}$.Using binomial approximation for small $\alpha \Delta 	heta$,$T' \approx T(1 + \frac{1}{2} \alpha \Delta 	heta)$.The fractional change in time period is $\frac{\Delta T}{T} = \frac{T' - T}{T} = \frac{1}{2} \alpha \Delta 	heta$.This expression is independent of the length $\ell$ of the pendulum. Therefore,statement $D$ is correct.

Similar Questions

Two simple pendulums of length $1\, m$ and $4\, m$ respectively are both given small displacement in the same direction at the same instant. They will be again in phase after the shorter pendulum has completed a number of oscillations equal to

The period of oscillation of a simple pendulum of length $L$ suspended from the roof of a vehicle which moves without friction down an inclined plane of inclination $\alpha$,is given by

If the time period of a $2 \ m$ long simple pendulum is $2 \ s$,the acceleration due to gravity at the place where the pendulum is executing $S.H.M.$ is

If the metal bob of a simple pendulum is replaced by a wooden bob, then its time period will

Vedclass Test Series

Exam Paper Generator

Online Exam Module