1

**Multiple Choice Questions**

The point at which the gravitational force acting on any mass is zero due to the Earth and the Moon system is (The mass of the Earth is approximately $81$ times the mass of the Moon and the distance between the Earth and the Moon is $3,85,000km$.)

If the mass of the Sun were ten times smaller and the universal gravitational constant were ten times larger in magnitude, which of the following is not correct?

Infinite number of bodies, each of mass 2 kg are situated on x-axis at distances 1m, 2m, 4m, 8m, , respectively, from the origin. The resulting gravitational potential due to this system at the origin will be -

A metal sphere has radius $R$ and mass $M$. A spherical hollow of diameter $R$ is made in this sphere such that its surface passes through the centre of the metal sphere and touches the outside surface of the metal sphere. A unit mass is placed at a distance from the centre of metal sphere. The gravitational field at that point is

A solid sphere of uniform density and radius $R$ applies a gravitational force of attraction equal to $F_{1}$ on a particle placed at a distance $2R$ from the centre of the sphere. A spherical cavity of radius $R/2$ is now made in the sphere as shown in the figure. The sphere with the cavity now applies a gravitational force $F_{2}$ on the same particle. The ratio $F_{1}/F_{2}$ is

The radius and density of two artificial satellites are $R_{1}$ , $R_{2}$ and $ρ_{1}$, $ρ_{2}$ respectively. The ratio of accelerations due to gravity on them will be:

The time period of a simple pendulum is T. When the length is increased by 10 cm, the period is $T_{1}$.When the length is decreased by 10 cm, its periodis T$_{2}$. Then relation between T, T$_{1}$, T$_{2}$ is

The angular velocity of the earth with which it has to rotate so that the acceleration due to gravity on $60_{∘}$ latitude becomes zero is

Two particles of masses $m$ and $2m$ are at a distance $3r$ apart at the ends of a straight line $AB$. $C$ is the centre of mass of the system. The magnitude of the gravitational intensity due to the masses at $C$ is

The figure shows the elliptical orbit of a planet P about the sun S. The shaded area SCD is a twice shaded area SAB. if $t_{1}$ is the the time for the planet to move from C to D and $t_{2}$ is the time to move from A to B, then