If the radius of the Earth were to shrink by | vedclass

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(D) The weight of an object of mass $m$ on the surface of the Earth is given by $W = mg = \frac{GM_e m}{R_e^2}$.When the radius of the Earth becomes h

Vedclass · Accepted Answer

It would become four times.

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(D) The weight of an object of mass $m$ on the surface of the Earth is given by $W = mg = \frac{GM_e m}{R_e^2}$.When the radius of the Earth becomes half $(R' = \frac{R_e}{2})$ while the mass $M_e$ remains constant,the new acceleration due to gravity $g'$ is:$g' = \frac{GM_e}{(R_e/2)^2} = \frac{GM_e}{R_e^2 / 4} = 4 \left( \frac{GM_e}{R_e^2} \right) = 4g$.Therefore,the new weight $W'$ is:$W' = mg' = m(4g) = 4W$.Thus,the weight of the object becomes $4$ times its original weight.

If the radius of the Earth were to shrink by half,its mass remaining the same,what would be the weight of an object on its surface?

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