First slide

Acceleration due to gravity and its variation

Question

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

Moderate

A

$5 {ms}^{- 2}$
B

$10 {ms}^{- 2}$
C

$3 {ms}^{- 2}$
D

$20 {ms}^{- 2}$

Solution

$F = (GMm) / R^{2} = mg$
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.

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