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  • If the radius of earth were to shrink by one percent, its mass remaining the same, the acceleration due to gravity on the earth’s surface would:  <stro

If the radius of earth were to shrink by one percent, its mass remaining the same, the acceleration due to gravity on the earth’s surface would:
 

Option: 1

decrease


Option: 2

remains unchanged
 


Option: 3

increase


Option: 4

None of these


Answers (1)

best_answer

\mathrm{ \mathrm{g}= \frac{\mathrm{GM}}{\mathrm{R}^2}}

\mathrm{\Rightarrow \frac{\mathrm{dg}}{\mathrm{g}}=-\frac{2 \mathrm{dR}}{\mathrm{R}} }

\mathrm{ \text { As } \frac{d R}{R}=-1 \% }

\mathrm{ \Rightarrow \frac{\mathrm{dg}}{\mathrm{g}}=-2(-1)=+2 \% }

Thus due to gravity will increase.

Hence option 3 is correct.
 

Posted by

vishal kumar

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