At a certain depth “” below surface of earth, value of acceleration due to gravity becomes four times that of its value at a height 3R above earth surface, where R is radius of earth (Take R = 6400 km). The depth is equal to [2023

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Solution

Q.
At a certain depth “ $d$ ” below surface of earth, value of acceleration due to gravity becomes four times that of its value at a height 3R above earth surface, where R is radius of earth (Take R = 6400 km). The depth $d$ is equal to [2023]

1 5260 km

2 640 km

3 2560 km

4 4800 km

Ans.
(4)

$\frac{G M}{R^{2}} [1 - \frac{d}{R}] = \frac{4 \times G M}{{(4 R)}^{2}}$

$1 - \frac{d}{R} = \frac{1}{4} \Rightarrow \frac{d}{R} = \frac{3}{4} \Rightarrow d = \frac{3}{4} R$

$d = 4800 km$

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