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The earth's radius shrinks by $10 %$ . By how much percent the acceleration due to gravity on the earth's surface would(mass remains constant) change?

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Decrease by

19 %

Increases by

19 %

Decreases by more than

19 %

Increases by more than

19 %

answer is D.

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Detailed Solution

The earth's radius shrinks by

10 %

. The acceleration due to gravity on the earth's surface would increase by more than

19 %

.
Let

R

be the radius of the Earth.
We know that the gravitational acceleration is then

g = \frac{GM}{R {^{2}}_{}} ​

The radius is now

0.9 R

, which is a

10 %

decrease.
As a result, the new gravitational acceleration is

g' = \frac{GM}{(0.9 R)^{2}} ​ ​

\Rightarrow g' = \frac{g}{(0.9)^{2}}

As a result, the increase in acceleration due to gravity is expressed as a

\Rightarrow g' - g = g (\frac{1}{(0.9)^{2}} - 1)

\Rightarrow

Percentage increase

= \frac{g' - g}{g} \times 100

Or, Percentage increase

= 23.45 %

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