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  4. The value of g at a particular point is 10 ms -2. Suppose the earth shrinks uniformly to half of its present size without losing any mass. The value of g at the same point (assuming that the distance of the point from the centre of the earth does not change) will now be

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Q. The value of $g$ at a particular point is $10\, ms ^{-2}$. Suppose the earth shrinks uniformly to half of its present size without losing any mass. The value of $g$ at the same point (assuming that the distance of the point from the centre of the earth does not change) will now be

Gravitation

Solution:

$F=(G M m) / R^{2}=m g$
As the mass remains the same and radius, i.e., distance from the centre is also the same, therefore $g$ will remain the same, i.e., $10\, m\, s ^{-2}$.