If the diameter of the earth becomes two time | vedclass

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(D) Let $M$ be the mass and $R$ be the radius of the earth.The weight of an object of mass $m$ on the surface of the earth is given by $W = mg = \frac

Vedclass · Accepted Answer

It will become one-fourth.

Vedclass · Answer

(D) Let $M$ be the mass and $R$ be the radius of the earth.The weight of an object of mass $m$ on the surface of the earth is given by $W = mg = \frac{GMm}{R^2}$.If the diameter becomes two times,the radius $R$ also becomes two times,i.e.,$R' = 2R$.The new weight $W'$ will be $W' = \frac{GMm}{(R')^2} = \frac{GMm}{(2R)^2} = \frac{GMm}{4R^2}$.Thus,$W' = \frac{1}{4} W$.Therefore,the weight of the object will become one-fourth of its original value.

If the diameter of the earth becomes two times its present value and its mass remains unchanged,then how would the weight of an object on the surface of the earth be affected?

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