Question

Assume there are two identical simple pendulum. 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 $4s$ and $6s$ respectively. Then the value of $h$ is -

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

• A. 1200 km
• B. 1600 km
• C. 3200 km
• D. 4800 km

Answer 1

Answer: (C)

3200 km

Answer 2

$t ∝ \frac{1} {\sqrt{g}}$ and $g∝ \frac{1}{(R + h)^2}$ $\frac{t1}{t2}$ = $\sqrt{\frac{g^1}{g}}$ = $\sqrt{\frac{R^2}{(R + h)^2}}$ $\frac{t1}{t2}$ = $\frac{4}{6}$ = $\frac{R}{(R + h)}$

⇒ $h = 3200km$