Question

The kinetic energy required to make a body move to infinity from earth surface is

Answer 1

answer is mgr.

escape velocity,v=(2gr)^1/2

ke=1/2(mv^2)

=mgr

Answer 2

The kinetic energy needed to move a body from the earth's surface to infinity is known as the escape energy of the body.

• If an object has escape velocity, it will never return to the earth, thus we may suppose it will travel an endless distance.
• We already know that the fleeing velocity is √2gR.
• Thus, the kinetic energy necessary to propel a body to infinity from the earth's surface is equal to half of the mass multiplied by the escape velocity squared.
• Mathematically, Kinetic energy = $\frac{1}{2} m (\sqrt{2gR})^2$  = mgR
• Thus, the kinetic energy needed to move a body from the earth's surface to infinity will be mgR, where m is the mass of the body and R is the radius of the earth.