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  • 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 <img alt="\mathrm{h}" src="https://entrancecorn

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 \mathrm{h} above the earth surface. Clock -1 and Clock - 2 operate at time periods 4 \mathrm{~s}$ and $6 \mathrm{~s} respectively. Then the value of \mathrm{h} is -
(consider radius of earth \mathrm{R_{E}=6400 \mathrm{~km} \: and \: g \: on \: earth \: 10 \mathrm{~m} / \mathrm{s}^{2}} )
 

Option: 1

1200 \mathrm{~km}


Option: 2

1600 \mathrm{~km}


Option: 3

3200 \mathrm{~km}


Option: 4

4800 \mathrm{~km}


Answers (1)

best_answer

\mathrm{T_1=4 S =2 \pi \sqrt{\frac{l}{g}} \rightarrow(1) }

\mathrm{T_2=6 S =2 \pi \sqrt{\frac{l}{g_h}} \rightarrow(2) }

\mathrm{g_h =\frac{g R^2}{(R+h)^2} \rightarrow(3) }

\mathrm{\frac{T_1}{T_2} =\frac{4}{6}=\sqrt{\frac{g_h}{g}} }

\mathrm{\frac{2}{3} =\sqrt{\frac{g_h}{g}} }

\mathrm{\frac{4}{9} =\frac{g_h}{g}=\frac{R^2}{(R+h)^2} }

\mathrm{\therefore h= \frac{R}{2}=3200 \mathrm{~km}}

Hence 3 is correct option






 

Posted by

Ajit Kumar Dubey

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