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

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)  (R/4)  (B)  (R/2)  (C)  (3R/4)  (D) None of these

Tardigrade Admin · Accepted Answer

At depth d, g=g(1-(d/R)) ∴ m g=m g(1-(d/R)) ⇒ (m g/4)=m g(1-(d/R))(A s, m g=(m g/4)) ⇒ (1/4)=1-(d/R) ⇒ (d/R)=1-(1/4)=(3/4) ∴ d=(3 R/4)

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

$\frac{R}{4}$

$\frac{R}{2}$

$\frac{3 R}{4}$

None of these

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

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

4R​

2R​

43R​