Question

If the earth suddenly shrinks (without changing mass) to half of its present radius, the acceleration due to gravity will be [MNR 1998]
A) g/2 B) 4g C) g/4 D) 2g

Answer 1

THE ANSWER IS --_-------------

B) 4 g



BECAUSE : g=GM/R^2
IF R REDUCES TO HALF g WILL INCREASE BY 4 BECAUSE IT IS INVERSELY PROPORTIONAL TO THE SQUARE OF RADIUS

Answer 2

Answer: The correct answer is 4g.

Explanation:

The expression for the acceleration due to gravity in terms of mass and radius of the earth is as follows;

$g= \frac{GM}{R^{2} }$                                 ......... (1)

Here, R is the radius of the earth, G is the universal gravitational constant and M is the mass of the object.

It is given in the problem that the earth suddenly shrinks (without changing mass) to half of its present radius. Then, the above equation (1) becomes as;

$g'=\frac{GM}{\frac{R}{2}^{2}}$

$g'=\frac{GM}{\frac{R^{2}}{4}}$

$g= 4\frac{GM}{R^{2}}$  

Compare the above equation with the equation (1).

$g'= 4g$

Therefore, the correct option is (B)