Question 1

Kepler's second law (law of areas) is a direct consequence of the law of conservation of:

Accepted Answer

Kepler's second law states that the line joining a planet to the Sun sweeps out equal areas in equal intervals of time. This is a direct consequence of the conservation of angular momentum.

Question 2

What is the dimensional formula of Universal Gravitational Constant ($G$)?

Accepted Answer

From $F = \frac{G m1 m2}{r^2}$, we get $G = \frac{F r^2}{m1 m2}$. Substituting dimensions: $G = \frac{M L T^{-2}L^2}{M^2} = M^{-1} L^3 T^{-2}$.

Question 3

The value of acceleration due to gravity ($g$) at the centre of the Earth is:

Accepted Answer

At a depth $d = R$ (centre of the Earth), $g' = g\left(1 - \frac{d}{R}\right) = g\left(1 - \frac{R}{R}\right) = 0$.

Question 4

The relation between escape velocity ($ve$) and orbital velocity ($vo$) for a satellite near the surface of Earth is:

Accepted Answer

Escape velocity is $ve = \sqrt{\frac{2GM}{R}}$ and orbital velocity is $vo = \sqrt{\frac{GM}{R}}$. Thus, $ve = \sqrt{2} vo$.

Question 5

If the distance between two masses is doubled, the gravitational force between them becomes:

Accepted Answer

Gravitational force $F \propto \frac{1}{r^2}$. If $r$ is doubled ($2r$), $F' = \frac{F}{2^2} = \frac{F}{4}$. Hence, it becomes one-fourth.