Question

How much deep inside the earth (radius $R$) should a mango, so that his weight becomes one-fourth of that on earths surface?

• A. $ \frac{R}{4} $
• B. $ \frac{R}{2} $
• C. $ \frac{3R}{4} $
• D. None of these

Answer 1

Answer: (C)

At depth $d, g=g\left(1-\frac{d}{R}\right)$
$\therefore m g=m g\left(1-\frac{d}{R}\right)$
$\Rightarrow \frac{m g}{4}=m g\left(1-\frac{d}{R}\right)\left(A s, m g=\frac{m g}{4}\right)$
$\Rightarrow \frac{1}{4}=1-\frac{d}{R}$
$\Rightarrow \frac{d}{R}=1-\frac{1}{4}=\frac{3}{4}$
$\therefore d=\frac{3 R}{4}$