When a ball is dropped from a height $\mathrm{h}$ it takes $\mathrm{t} \mathrm{sec}$ to reach the ground. If…
When a ball is dropped from a height $\mathrm{h}$ it takes $\mathrm{t} \mathrm{sec}$ to reach the ground. If the same experiment in done on a different planet having the mass 100 times the earth's mass and radius 10 times the earth's radius, then the time it will take to cover the same height in the new planet is
ts
$100 \mathrm{ts}$
$\frac{\mathrm{t}}{100} \mathrm{~s}$
$\frac{\mathrm{t}}{10} \mathrm{~s}$
Solution
We have,
$\mathrm{g}_{\text {earth }}=\sqrt{\frac{\mathrm{GM}}{\mathrm{R}^2}}$
$\mathrm{g}_{\text {planet }}=\sqrt{\frac{\mathrm{G} \times 100 \mathrm{M}}{(10 \mathrm{R})^2}}=\sqrt{\frac{\mathrm{GM}}{\mathrm{R}^2}}=\mathrm{g}_{\text {earth }}$
As $g_{\text {planet }}=g_{\text {earth }}$. So time taken to cover 'h' height will be same as that on earth.