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

Answer: (D)

225 N

Answer 2

At the surface:
$mg = 300 \, \text{N}$
$m = \frac{300}{g_s}$
At depth $\frac{R}{4}$:
$g_d = g_s \left( 1 - \frac{d}{R} \right)$
where $d = \frac{R}{4}$.
$g_d = g_s \left( 1 - \frac{R}{4R} \right) = g_s \cdot \frac{3}{4}$
The weight at depth $\frac{R}{4}$ is:
$\text{Weight} = m \times g_d = m \times \frac{3 g_s}{4}$
$= \frac{3}{4} \times 300 = 225 \, \text{N}$