Question

The value of $g$ at a particular point on the earth surface is $9.8m{s}^{-2}$. Suppose the earth suddenly shrinks uniformly to half 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 earth does not shrink) will now be:

• A. $4.9m{s}^{-2}$
• B. $3.1m{s}^{-2}$
• C. $9.8m{s}^{-2}$
• D. $19.6m{s}^{-2}$

Answer 1

The correct option is C $9.8m{s}^{-2}$

The mathematical equation of acceleration due to gravity is given as,
$g=\frac{GM}{r^2}$
where, $G$ is the universal gravitational constant, $M$ is the mass od the planet and $r$ is the distance between object and center of gravity.
Since, $G$, $M$ and $r$ are constant, the value of $g$ will remain same.
That is, $g=9.8m{s}^{-2}$.