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 4s and 6s respectively. Then the value of h is – (consider radius of earth R_E = 6400km and g on earth 10 m/s²)

Option 1 - 1200 km

Option 2 - 1600 km

Option 3 - 3200 km

Option 4 - 4800 km

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Vishal Baghel | Contributor-Level 10

6 months ago

Correct Option - 3

Detailed Solution:

$\frac{T_{1}}{T_{2}} = \frac{4}{6} = \sqrt[]{\frac{g_{2}}{g_{1}}}$

$\Rightarrow {(1 + \frac{h}{R})}^{2} = \frac{9}{4} \Rightarrow 1 + \frac{h}{R} = \frac{3}{2} \Rightarrow h = \frac{R}{2} = 3200 k m .$

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