Question 122: Gravitation

Question

If the radius of earth shrinks by $$2 \%$$ while its mass remains same. The acceleration due to gravity on the earth's surface will approximately :

Accepted Answer

The acceleration due to gravity (g) on the surface of a planet is given by the formula:
$$g = \frac{G M}{R^2}$$
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:
$$g' = \frac{G M}{(0.98R)^2} = \frac{G M}{0.9604 R^2} = \frac{g}{0.9604}$$
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%.

Answer

decrease by $$2 \%$$

Answer

decrease by $$4 \%$$

Answer

increase by $$2 \%$$

Answer

increase by $$4 \%$$

Gravitation

If the radius of earth shrinks by $2 \%$ while its mass remains same. The acceleration due to gravity on the earth's surface will approximately :

Choose the correct answer: