(C) The weight of an object on the surface of the Earth is given by $W = mg = \frac{GM_e m}{R_e^2}$.When the radius of the Earth is doubled,the new ra

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(C) The weight of an object on the surface of the Earth is given by $W = mg = \frac{GM_e m}{R_e^2}$.When the radius of the Earth is doubled,the new radius becomes $R_e' = 2R_e$.The new weight $W'$ is given by $W' = \frac{GM_e m}{(2R_e)^2} = \frac{GM_e m}{4R_e^2}$.Substituting the original weight $W$ into the equation,we get $W' = \frac{W}{4}$.Therefore,the weight of the object becomes one-fourth of its original weight.

Class 11 Physics Gravitation Acceleration Due to Gravity and its Variation

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If the radius of the Earth becomes double while its mass remains unchanged,what will be the change in the weight of an object of mass $m$ on the surface of the Earth?

A
It becomes double.
B
It becomes half.
C
It becomes one-fourth.
D
It remains the same.

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Gravitation

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Acceleration Due to Gravity and its Variation

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If the radius of the Earth becomes double while its mass remains unchanged,what will be the change in the weight of an object of mass $m$ on the surface of the Earth?

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