If the earth suddenly shrinks (without changi | vedclass

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(B) The acceleration due to gravity $g$ on the surface of the Earth is given by the formula $g = \frac{GM}{R^2}$,where $G$ is the gravitational consta

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$4g$

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(B) The acceleration due to gravity $g$ on the surface of the Earth is given by the formula $g = \frac{GM}{R^2}$,where $G$ is the gravitational constant,$M$ is the mass of the Earth,and $R$ is its radius.Since the mass $M$ remains constant and the radius shrinks to half of its present value,let the new radius be $R' = \frac{R}{2}$.The new acceleration due to gravity $g'$ will be $g' = \frac{GM}{(R')^2} = \frac{GM}{(R/2)^2} = \frac{GM}{R^2/4} = 4 \left( \frac{GM}{R^2} \right) = 4g$.Therefore,the acceleration due to gravity becomes four times its present value.

If the earth suddenly shrinks (without changing mass) to half of its present radius,the acceleration due to gravity will be

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