Assume there are two identical simple pendulum clocks. Clock - 1 is… | JEE Main 2022 (28 Jul, Shift 2)

Q56JEE Main 2022 · 28 JUL · SHIFT 2Medium

Simple Pendulum

Assume there are two identical simple pendulum clocks. Clock - 1 is placed on the earth and Clock - 2 is placed on a space station located at a height h above the earth surface. Clock - 1 and Clock - 2 operate at time periods 4 s and 6 s respectively. Then the value of h is -

(consider radius of earth $R_E = 6400\text{ km}$ and $g$ on earth $10\text{ m/s}^{2}$ )

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Answer: (c)

$T \propto \frac{1}{\sqrt{g}}$ and $g \propto \frac{1}{(R+h)^2}$ , so $T \propto (R+h)$ .
$\frac{T_2}{T_1} = \frac{6}{4} = \frac{R+h}{R} \Rightarrow h = 0.5R$ .
$h = 0.5 \times 6400 = 3200\text{ km}$ .
So the answer is (c) 3200 km.

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