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If the Earth suddenly shrinks to half of its present radius, then the acceleration due to gravity will be

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g

6 g

4 g

10 g

answer is C.

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Detailed Solution

If the Earth suddenly shrinks to half of its present radius, then the acceleration due to gravity will be

4 g

.
It is known that the acceleration due to gravity on the surface of the earth is given by

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

Where

R =

radius of earth

G =

universal gravitational constant

M =

mass of earth
it is given that the radius of the earth becomes half of its value then radius becomes

R_{1} = \frac{R}{2}

and the acceleration due to gravity

g_{1}

is given by

\Rightarrow g_{1} = \frac{GM}{R_{1}^{2}}

\Rightarrow g_{1} = \frac{GM}{{(\frac{R}{2})}^{2}}

\Rightarrow g_{1} = \frac{GM}{R^{2}} \times 4

{\Rightarrow g}_{1} = 4 g

Hence, the acceleration due to gravity becomes

4

times when the radius of earth shrinks to half of its radius.

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If the Earth suddenly shrinks to half of its present radius, then the acceleration due to gravity will be

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