Gravitation Question 12
Question 12 - 31 January - Shift 1
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 $3 R$ above earth surface. Where $R$ is Radius of earth (Take $R=6400 km$ ). The depth $d$ is equal to
(1) $5260 km$
(2) $640 km$
(3) $2560 km$
(4) $4800 km$
Show Answer
Answer: (4)
Solution:
Formula: Effect of depth
$ \begin{aligned} & \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 \end{aligned} $
