A body weighs 45 N on the surface of the earth. The gravitational force on a body due to earth at a height equal to half the radius of earth will be

The weight $W = 45\,\text{N}$ on Earth's surface satisfies $W = \frac{GMm}{R^2}$.

At height $h = R/2$, the gravitational force becomes $F' = \frac{GMm}{(R + h)^2} = \frac{GMm}{(3R/2)^2} = \frac{4}{9} \cdot \frac{GMm}{R^2}$.

Substituting the expression for weight yields $F' = \frac{4}{9}W = \frac{4}{9} \cdot 45 = 20\,\text{N}$.

The gravitational force at half Earth's radius is $20\,\text{N}$.