Question

An object of mass m is dropped from a height h above the surface of a planet of mass M and radius R. Find the speed of the object when it hits the planet surface. Enter your answer as an expression in terms of m, M, R, h and the universal constant of gravity G.

Answer 1

Answer:

$v=\sqrt{\frac{2GMh}{R^{2}}}$

Explanation:

mass of object = m

Mass of planet = M

Radius of planet = R

Height = h

Let the speed of the object as it hits the earth's surface is v.

the value of acceleration due to gravity

g = G M / R^2

where, g is the universal gravitational constant.

Use third equation of motion

$v^{2}=u^{2}+2gh$

where, u is the initial velocity which is equal to zero.

So, $v^{2}=0 + 2 \times \frac{GM}{R^{2}}\times h$

$v=\sqrt{\frac{2GMh}{R^{2}}}$