JEE Main 2022 — Gravitation Question with Solution

The acceleration due to gravity (g) on the surface of a planet is given by the formula:

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

where:

• G is the gravitational constant,
• M is the mass of the planet,
• R is the radius of the planet.

If the radius of the Earth shrinks by 2% but its mass remains the same, the new acceleration due to gravity (g') will be:

$$g^{\prime }=\frac{GM}{(0.98R{)}^2}=\frac{GM}{0.9604R^2}=\frac{g}{0.9604}$$

This implies that g' is approximately 1.0412 times g, or an increase of approximately 4.12%.

Therefore, the acceleration due to gravity on the Earth's surface will approximately increase by 4%.