Question

Assuming the earth to be a sphere of uniform density the gravitational field

• A. at a point outside the earth is inversely proportional to the square of its distance from the centre.
• B. at a point outside the earth is inversely proportional to its distance from the centre.
• C. at a point inside is zero.
• D. at a point inside is proportional to square of its distance from the centre.

Answer 1

The correct option is A at a point outside the earth is inversely proportional to the square of its distance from the centre.

Gravitational field inside a solid sphere of mass $M$ and radius $R$ at distance $x$ is given by, $$E=\frac{GMx}{R^3}$$ Since, the Earth can be assumed to be a solid sphere, so the gravitational field inside the Earth at distance $x$ from its centre, due to its mass within is $$E\propto x$$so, at a point inside the surface of earth gravitational field intensity is proportional to its distance from the centre.

Gravitational field outside a solid sphere of mass $M$ and radius $R$ at distance $x$ is given by, $$E=\frac{GM}{x^2}$$ Hence, $E\propto \frac{1}{x^2}$

So, at a point outside the earth gravitational field intensity is inversely proportional to the square of its distance from the centre.

Hence, option (a) is the correct answer.