If the radius of earth decreases by $10$ %, the mass remaining unchanged, what will happen to 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 D Increases by more than $19$ %
$g = \frac{G M}{R^{2}}$

$g^{'} = \frac{G M}{{\frac{81 R}{100}}^{2}}$ because R' = $\frac{9 R}{10}$

So, $\frac{g^{'} - g}{g} * 100 = 23 %$ So, acceleration due to gravity increases by more than 19%.

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

The correct option is D Increases by more than 19 %g=GMR2g′=GM81R1002 because R' = 9R10So, g′−gg∗100=23% So, acceleration due to gravity increases by more than 19%.

If the radius of earth decreases by $10$ %, the mass remaining unchanged, what will happen to the acceleration due to gravity?

The correct option is D Increases by more than $19$ %
$g = \frac{G M}{R^{2}}$

$g^{'} = \frac{G M}{{\frac{81 R}{100}}^{2}}$ because R' = $\frac{9 R}{10}$

So, $\frac{g^{'} - g}{g} * 100 = 23 %$ So, acceleration due to gravity increases by more than 19%.