The value of 'g' at a particular point is 9.8m/s². 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

The correct option is 9.8m / sec².

Let us understand the physical principles behind this result step-by-step.

The acceleration due to gravity, $g$, at any point outside or on the surface of the Earth is given by Newton's law of universal gravitation:
$g=\frac{GM}{r^2}$
where:
• $G$ is the universal gravitational constant,
• $M$ is the mass of the Earth, and
• $r$ is the distance of the point from the center of the Earth.

According to the problem statement:
1. The Earth shrinks uniformly to half its present size, but it does not lose any mass. Therefore, the mass of the Earth, $M$, remains constant ($M^{\prime }=M$).
2. The distance of the point from the center of the Earth does not shrink. Thus, the distance $r$ remains exactly the same ($r^{\prime }=r$).
3. The gravitational constant, $G$, is a universal constant and does not change.

Since none of the variables ($G$, $M$, and $r$) determining the value of $g$ at that particular point have changed, the value of the acceleration due to gravity at that point will remain completely unaffected.

Therefore, the value of $g$ at the same point will still be:
$g^{\prime }=g=9.8{\text{m/s}}^2$ (or 9.8m / sec²).