Question

A body is dropped from a height equal to the radius of the Earth, M is the mass of the Earth. R is the radius of the Earth. The velocity of the body on reaching the surface of Earth will be

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

$\text{Applying conservation of energy}.-\frac{GMm}{2R}+0=\frac{1}{2}m{v}^2-\frac{GMm}{R}or\frac{1}{2}m{v}^2=\frac{GMm}{R}-\frac{GMm}{2R}or\frac{1}{2}m{v}^2=\frac{GMm}{2R}orv=\sqrt{\frac{GM}{R}}$