Question

Find the height at which the weight will be same as at the same depth from the surface of the earth.

• A. $\frac{R}{2}$
• B. $\sqrt{5}R-R$
• C. $\frac{\sqrt{5}R-R}{2}$
• D. $\frac{\sqrt{3}R-R}{2}$

Answer 1

Answer: (C)

$\frac{\sqrt{5}R-R}{2}$

Let the height and depth be 'd'

$\Rightarrow \frac{g}{{(1+\frac{d}{R})}^2}=g(1-\frac{d}{R})$

$\Rightarrow {(1+\frac{d}{R})}^2(1-\frac{d}{R})=1$

$\Rightarrow (1+\frac{d^2}{R^2}+\frac{2d}{R})(1-\frac{d}{R})=1\Rightarrow {\left(\frac{d}{R}\right)}^3+{\left(\frac{d}{R}\right)}^2-\left(\frac{d}{R}\right)=0\Rightarrow d=\frac{\sqrt{5}R-R}{2}$