Question

What should be the projection velocity for a body to reach the same height on the Moon as compared to that on the Earth?

• A. Higher velocity on the moon
• B. Lower velocity on the moon
• C. Same velocity on the moon and earth.
• D. It depends on the mass of the body

Answer 1

The correct option is B Lower velocity on the moon

Let u be the velocity to project a body up to reach height h.
Then by equation $v^2=u^2-2gh$, we get:

$0=u^2-2gh$, since $v=0$
$\Rightarrow$ $u=\sqrt{2gh}$
Now we know acceleration due to gravity for moon$=\frac{g}{6}$ (approx)
So to reach same height $h$, velocity required would be $u^{\prime }=\sqrt{\frac{2gh}{6}}=\sqrt{\frac{gh}{3}}$
Thus from above we can see that the velocity required to throw a body vertically up to same height $h$ on moon is less than velocity required on earth.