Question

A body weighs $500N$ on the surface of the earth. How much would it weigh halfway below the surface of the earth?

• A. $125N$
• B. $250N$
• C. $500N$
• D. $1000N$

Answer 1

The correct option is B

$250N$

Step 1. Given data: Weight, $W$ at the surface of earth $=500N$

Step 2. The formula used: Apparent acceleration halfway below the surface of the earth, $g^{\text{'}}=g(1-\frac{h}{R})$where,$h$ is the height below the surface of the earth, $R$is the radius of the earth, $g$is the acceleration due to gravity.

Step 3: Calculate the apparent weight at the equator,

$W^{\text{'}}=W(1-\frac{h}{R})$

At halfway below the surface of the earth, $h=\frac{R}{2}$

So, $W^{\text{'}}=500(1-\frac{R/2}{R})$ $=500(1-\frac{1}{2})$$N$= $250N$

Hence, the weight of the body halfway below the surface of the earth is $250N$.

Option B is correct.