### 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} $