If both mass and radius of earth decrease by 1% , value of acceleration due to gravity will

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7.Gravitation

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If both the mass and the radius of the earth decrease by $1\%$ , the value of the acceleration due to gravity will

A

decrease by $1\%$

B

increase by $1\%$

C

increase by $2\%$

D

remain unchanged

Solution

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

$\frac{\mathrm{dg}}{\mathrm{g}} \times 100 \%=\frac{\mathrm{dM}}{\mathrm{M}} \times 100 \%-2 \frac{\mathrm{d} \mathrm{R}}{\mathrm{R}} \times 100 \%$

$=-1-2(-1)$

$=-1+2=1 \%$

Standard 11

Physics

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