Q. If both the mass and radius of Earth decrease by $1 \%$, the value of acceleration due to gravity will change by nearly :

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A

$1 \%$ decrease

50%

B

$1.5 \%$ increase

0%

C

$1 \%$ increase

33%

D

$2 \%$ decrease

17%

Solution:

Acceleration due to gravity is given as $g=G M / R^{2}$ and on changing the mass to $0.99\, M$ and $R$ to $0.99 \,R$ the result will be changed as $g^{\prime}=1.01 \,G M / R^{2}$ hence option (C) is correct.

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