Question

The weight of the body at earth's surface is W. At a depth halfway to the center of the earth, it will be? (assuming uniform density in the earth)

• A. $W$
• B. $\frac{W}{2}$
• C. $\frac{W}{3}$
• D. $\frac{W}{8}$

Answer 1

The correct option is B $\frac{W}{2}$

$G^1=g(1-\frac{d}{R})⟶\left(1\right)$

Now $d$ that is depth is $\frac{R}{2}$ substituting $d=\frac{R}{2}$ in eq $\left(1\right)$

$G^1=g(1-\frac{R}{2R})=g(1-\frac{1}{2})=\frac{g}{2}$

So, $g^1=\frac{g}{2}$

Multiplying both sides by $M$

${mg}^1=\frac{mg}{2}$

Weight is nothing but mass $\times$ gravity

Weight at half way depth $=\frac{W}{2}$