Question

Assuming the earth to be a sphere of uniform mass density, a body weighed 300 N on the surface of earth. How much it would weigh at R/4 depth under surface of earth ?

• A. 75 N
• B. 375 N
• C. 300 N
• D. 225 N

Answer 1

The Correct Option is D

Surface gravitational force: \[mg = 300 \, \text{N}\]
Mass: \[m = \frac{300}{g_s}\]
Gravitational acceleration at depth \( \frac{R}{4} \):
\[g_d = g_s \left( 1 - \frac{d}{R} \right)\]
Given \( d = \frac{R}{4} \).
\[g_d = g_s \left( 1 - \frac{R}{4R} \right) = g_s \cdot \frac{3}{4}\]
Weight at depth \( \frac{R}{4} \) is:
\[\text{Weight} = m \times g_d = m \times \frac{3 g_s}{4}\]
\[= \frac{3}{4} \times 300 = 225 \, \text{N}\]