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  4. The value of g at a particular point is 9.8 ms-2. Suppose theearth suddenlyshrinks uniformly to half its present size without losing any mass. The value ofg at the same point (distance of the point from the centre of earth does not change) will now be

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Q. The value of g at a particular point is $9.8 \, ms^{-2}$. Suppose theearth suddenlyshrinks uniformly to half its present size without losing any mass. The value ofg at the same point (distance of the point from the centre of earth does not change) will now be

AIIMSAIIMS 2013

Solution:

If $g_i$ be the initial value tor acceleration aue to gravity and $g_f$, be the final value then
$g_{i}=\frac{G M}{R^{2}}=g$ and
$g_{f}=\frac{G M}{\left(\frac{R}{2}+\frac{R}{2}\right)^{2}}=g$
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