A simple pendulum doing small oscillations at a place R height above earth surface has time period of T_1=4 ~s . T_2 would be it's time period if it is brought to a point which is at a height 2 R from earth surface.

Correct answer: D. 3 ~T_1=2 ~T_2 aligned & T_1=2 π GM (2 R)^2 & ~T_2=2 π GM (3 R)^2 & T_1 ~T_2 =(2)/(3) aligned

JEE Main 20245 AprilMorning Shift

JEE Main 2024 · 5 April · Morning Shift · Physics · Gravitation

A simple pendulum doing small oscillations at a place R height...

A simple pendulum doing small oscillations at a place

\mathrm{R}

height above earth surface has time period of

T_1=4 \mathrm{~s}

T_2

would be it's time period if it is brought to a point which is at a height

2 \mathrm{R}

from earth surface. Choose the correct relation

[R=

radius of earth

]

D. $3 \mathrm{~T}_1=2 \mathrm{~T}_2$

\begin{aligned} & \mathrm{T}_1=2 \pi \sqrt{\frac{\ell}{\mathrm{GM}}(2 \mathrm{R})^2} \\ & \mathrm{~T}_2=2 \pi \sqrt{\frac{\ell}{\mathrm{GM}}(3 \mathrm{R})^2} \\ & \therefore \frac{\mathrm{T}_1}{\mathrm{~T}_2}=\frac{2}{3}\end{aligned}