T is the time period of simple pendulum on the earth's surface. Its time period becomes x T when taken to a height R (equal to earth's radius) above the earth's surface. Then, the value of x will be:
Select the correct option:
A
4
B
2
C
$\frac{1}{2}$
D
$\frac{1}{4}$
✓ Correct! Well done.
✗ Incorrect. Try again or view the solution.
Solution
Sol. At surface of earth time period
$$
\mathrm{T}=2 \ell \sqrt{\frac{\ell}{\mathrm{~g}}}
$$
At height $h=R \mid$
$\begin{array}{ll} & g^{\prime}=\frac{g}{\left(1+\frac{h}{R}\right)^2}=\frac{g}{4} \\ \therefore & \mathrm{xT}=2 \pi \sqrt{\frac{\ell}{(g / 4)}} \\ \Rightarrow & \mathrm{xT}=2 \times 2 \pi \sqrt{\frac{\ell}{g}} \\ \Rightarrow & \mathrm{xT}=2 \mathrm{~T} \Rightarrow \mathrm{x}=2\end{array}$
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