Question

A body weighs 300 N on the surface of the earth. How much will it weigh at a distance $\frac{R}{2}$ below the surface of earth? ($R \rightarrow$ Radius of earth)

• A. 300 N
• B. 250 N
• C. 200 N
• D. 150 N

Hint:

Logic Tip: At exactly halfway to the Earth's center, the gravitational pull is reduced by half.

Answer 1

The Correct Option is D

Concept:
Acceleration due to gravity varies linearly with depth below the Earth's surface.
Step 1: Use the formula for gravity at depth.
The acceleration due to gravity at depth $d$ is: $$g_{d}=g(1-\frac{d}{R})$$
Step 2: Substitute the given depth.
Given $d = \frac{R}{2}$: $$g_{d}=g(1-\frac{1}{2}) = \frac{g}{2}$$
Step 3: Calculate the new weight.
The weight of the body at depth $d$ is: $$W_{d}=mg_{d}=300\times\frac{1}{2}=150~N$$