A boy weighs 72 N on the surface of earth. The gravitational force on a body due to earth at a height equal…
A boy weighs 72 N on the surface of earth. The gravitational force on a body due to earth at a height equal to half the radius of earth will be
32 N
48 N
96 N
162 N
Solution
At height $\left(\mathrm{h}=\frac{\mathrm{R}}{\mathrm{n}}\right)$, the value of acceleration due to gravity is given by, $\mathrm{g}_{\mathrm{h}}=\left(\frac{\mathrm{n}}{\mathrm{n}+1}\right)^2 \mathrm{~g}$.
For $\mathrm{n}=2$,
$\begin{aligned}
& \mathrm{g}_{\mathrm{h}}=\left(\frac{\mathrm{n}}{\mathrm{n}+1}\right)^2 \mathrm{~g}=\left(\frac{2}{2+1}\right)^2 \mathrm{~g}=\frac{4}{9} \mathrm{~g} \\
& \mathrm{~W}_{\mathrm{h}}=\mathrm{mg}_{\mathrm{h}}=\frac{4}{9} \times \mathrm{mg}=\frac{4}{9} \times 72=32 \mathrm{~N}
\end{aligned}$