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

Is the oscillation of a simple pendulum at the centre of the earth possible?

The force constant of an oscillating simple pendulum is

An object of mass $3 \,kg$ is tied by a string of negligible mass to a ceiling and held such that the string is taut. The object is released suddenly such that the string remains taut. Its acceleration when released is (acceleration due to gravity $= 10 \,ms^{-2}$) (in $\,ms^{-2}$)

The bob of a simple pendulum is a spherical hollow ball filled with water. $A$ plugged hole near the bottom of the oscillating bob gets suddenly unplugged. During observation,till water is coming out,the time period of oscillation would

$A$ simple pendulum is released from rest at the horizontally stretched position. When the string makes an angle $\theta$ with the vertical,the angle $\phi$ which the acceleration vector of the bob makes with the string is given by

Vedclass Test Series

Exam Paper Generator

Online Exam Module