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7.Gravitation
hard
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 $2 R$ from earth surface. Choose the correct relation $[R=$ radius of Earth]:
A
$\mathrm{T}_1=\mathrm{T}_2$
B
$2 \mathrm{~T}_1=3 \mathrm{~T}_2$
C
$3 \mathrm{~T}_1=2 \mathrm{~T}_2$
D
$2 \mathrm{~T}_1=\mathrm{T}_2$
(JEE MAIN-2024)
Solution
$\mathrm{T}_1=2 \pi \sqrt{\frac{\ell}{\mathrm{GM}}(2 \mathrm{R})^2}$
$\mathrm{~T}_2=2 \pi \sqrt{\frac{\ell}{\mathrm{GM}}(3 \mathrm{R})^2}$
$\therefore \frac{\mathrm{T}_1}{\mathrm{~T}_2}=\frac{2}{3}$
Standard 11
Physics
