## Numerical

Two spherical stars $A$ and $B$ have densities $\rho_{A}$ and $\rho_{B}$, respectively. $A$ and $B$ have the same radius, and their masses $M_{A}$ and...

The distance between two stars of masses 3MS and 6MS is 9R. Here R is the mean distance between the centers of the Earth and the Sun, and MS is the ma...

A large spherical mass M is fixed at one position and two identical masses m are kept on a line passing through the centre of M (see figure). The poin...

A bullet is fired vertically upwards with velocity v from the surface of a spherical planet. When it reaches
its maximum height, its acceleration due ...

A binary star consists of two stars A (mass 2.2Ms) and B (mass 11Ms), where Ms is the mass of the sun. They are separated by distance d and are rotati...

Gravitational acceleration on the surface of a planet is $${{\sqrt 6 } \over {11}}g$$, where $$g$$ is the gravitational acceleration on
the surface of...

## MCQ (Single Correct Answer)

Consider a spherical gaseous cloud of mass density $$\rho $$(r) in free space where r is the radial distance from its center. The gaseous cloud is mad...

A planet of mass $$M,$$ has two natural satellites with masses $${m_1}$$ and $${m_2}.$$ The radii of their circular orbits are $${R_1}$$ and $${R_...

A rocket is launched normal to the surface of the Earth, away from the sun, along the line joining the Sun and the Earth. The Sun is $$3 \times 10{}^5...

A planet of radius R = $${1 \over {10}} \times $$ (radius of Earth) has the same mass density as Earth. Scientists dig a well of
depth $${R \over 5}$$...

A satellite is moving with a constant speed ‘V’ in a circular orbit about the earth. An object of mass ‘m’ is
ejected from the satellite such that it ...

A thin uniform annular disc (see figure) of mass M has outer radius 4R and inner radius 3R. The work required to take a unit mass from point P on its ...

## MCQ (More than One Correct Answer)

Two bodies, each of mass M, are kept fixed with a separation $$2L$$. A particle of mass m is projected from
the midpoint of the line joining their cen...

Two spherical planets P and Q have the same uniform density r, masses MP and MQ and surface
areas A and 4A respectively. A spherical planet R also has...