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Question

If the radius of the earth decreases by 10%, the mass remaining unchanged, then acceleration due to gravity will

A
decreases by 19 %
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B
increases by 19 %
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C
decreases by more than 19 %
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D
increases by more than 19 %
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Solution

The correct option is D increases by more than 19 %
Acceleration due to gravity
g=GMR2

as given, radius is decreased by 10 %.
so R=0.9R

Now, new acceleration due to gravity g=GM(0.9R)2

gg=GM(0.9R)2GMR2gg=10.81g=1.23g

So acceleration due to gravity is increased by 23%.

Hence, option D is correct.

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