If the radius of earth shrinks by 2% while its mass remains same. The acceleration due to gravity on the earth's surface will approximately:

Option 1 - Decrease by 2%

Option 2 - Decrease by 4%

Option 3 - Increase by 2%

Option 4 - Increase by 4%

2 Views|Posted 8 months ago

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Answered by

Vishal Baghel | Contributor-Level 10

8 months ago

Correct Option - 4

Detailed Solution:

$g = \frac{G M}{r^{2}}$

$d g = - 2 \frac{G M}{r^{3}} d r$

$\Rightarrow d g * 100 = - 2 (\frac{G M}{r^{2}}) \frac{d r}{r} * 100$

$\Rightarrow \frac{d g}{g} * 100 = \underset{}{\underset{?}{- 2 * 2}} = - 4 %$

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