Question

On the earth, when an astronaut throws a 0.250 kg stone vertically upward, it returns to his hand a time T later. On planet X he finds that, under the same circumstances, the stone returns to his hand in 2T. In both cases, he throws the stone with the same initial velocity and it feels negligible air resistance. What is the acceleration due to gravity on planet X (in terms of g)?

Answer 1

Answer:$\frac{g}{2}$

Explanation:

Given

mass of stone$\left ( m\right )$=0.250 kg

Let initial velocity with which it is thrown upward is u

therefore after time t it's velocity is zero at highest point

t=$\frac{u}{g}$

where g= gravity at earth

therefore $T=2\times \frac{u}{g}$-------1

Now same thing is done in Planet X where gravity is g'

therefore time taken by stone to reach surface is

$T'=T=2\times \frac{u}{g'}$-------2

Divide 1 & 2

$\frac{T}{T'}$=$\frac{g'}{g}$

$\frac{1}{2}$=$\frac{g'}{g}$

g'=$\frac{g}{2}$