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 :

Answer:

[tex]v=\sqrt{\frac{2GMh}{R^{2}}}[/tex]

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

[tex]v^{2}=u^{2}+2gh[/tex]

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

So, [tex]v^{2}=0 + 2 \times \frac{GM}{R^{2}}\times h[/tex]

[tex]v=\sqrt{\frac{2GMh}{R^{2}}}[/tex]

Other Questions