Question

Assuming the earth to be a sphere of a uniform mass density, how much would a body weigh half way down to the center of earth if it weighed 250 N on the surface? }

• A. 375 N
• B. 125 N
• C. 500 N
• D. 72.5 N

Hint:

Gravity inside a uniform sphere decreases linearly with distance from the center.

Answer 1

The Correct Option is B

Step 1: Concept
Acceleration due to gravity at depth $d$ is $g' = g(1 - d/R)$.
Step 2: Analysis
Weight on surface ($W$) = $mg = 250$ N. Depth ($d$) = $R/2$ (half way down).
Step 3: Calculation
$g' = g(1 - (R/2)/R) = g(1 - 1/2) = g/2$. Weight at depth ($W'$) = $mg' = mg/2 = 250 / 2 = 125$ N.
Step 4: Conclusion
Hence, the body weighs 125 N.
Final Answer:(B)