Q112 / 150 · MHT CET 2022 (10 Aug Shift 2) · Physics
A body weights 500 Non the surface of earth. At what distance below the surface of earth it weight $250 \mathrm{~N}$ ?
(Radius of earth, $R=6400 \mathrm{~km}$ )
- A$800 \mathrm{~km}$
- Correct answerB32000 km
- C$1600 \mathrm{~km}$
- D$6400 \mathrm{~km}$
Solution
Value of acceleration due to gravity decreases on going below the surface of the earth. Weight $(w)$ of a body is defined as product of mass $(m)$ and acceleration due to gravity $w=m g$.
The value of g below the surface of earth at a distance $h$ is given by,
$\begin{aligned} & g^{\prime}=g\left(1-\frac{h}{R}\right) \\ & \Rightarrow W^{\prime}=W\left(1-\frac{h}{R}\right)\end{aligned}$
Given, $W^{\prime}=250 \mathrm{~N}$ and $W=500$
$\begin{aligned} & 250=500\left(1-\frac{h}{R}\right) \\ & \Rightarrow h=\frac{R}{2}=32000 \mathrm{~km}\end{aligned}$
Hence, the correct answer is option: 'B'.