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

decreases by

19 %

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increases by

19 %

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decreases by more than

19 %

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increases by more than

19 %

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Solution

The correct option is A increases by more than $19 %$
The acceleration due to gravity is given by:
$g = \frac{G M}{R^{2}}$
$\Rightarrow g \propto \frac{1}{R^{2}}$
$\Rightarrow \frac{Δ g}{g} = - 2 \frac{Δ R}{R} = - 2 (- 0.1) = 0.2$
So, the value of $g$ increases by $20 %$ .

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

The correct option is A increases by more than 19%The acceleration due to gravity is given by: g=GMR2⇒g∝1R2⇒Δgg=−2ΔRR=−2(−0.1)=0.2So, the value of g increases by 20%.

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

The correct option is A increases by more than $19 %$
The acceleration due to gravity is given by:
$g = \frac{G M}{R^{2}}$
$\Rightarrow g \propto \frac{1}{R^{2}}$
$\Rightarrow \frac{Δ g}{g} = - 2 \frac{Δ R}{R} = - 2 (- 0.1) = 0.2$
So, the value of $g$ increases by $20 %$ .