BITSAT 2024 Shift 1 Paper

To determine the velocity of a body falling from rest at a height R above the Earth's surface, we must equate the increase in kinetic energy to the decrease in potential energy.
Given:
Initial height h=R
Radius of Earth R
Acceleration due to gravity g
The change in potential energy when the body falls to the Earth's surface can be given by:
∆U=‌

mgh

1+‌ h R

Substituting h=R, we get:
∆U=‌

mgR

1+‌ R R

=‌

mgR

2

By the conservation of energy principle, the increase in kinetic energy equals the decrease in potential energy:
‌

1

2

mv2=‌

mgR

2

Solving for v :
‌mv2=mgR
‌v2=gR
‌v=√gR
Thus, the velocity of the body when it reaches the Earth's surface is v=√gR.