# NCERT Class 11 Physics Solutions: Chapter 8 – Gravitation-Part 8

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Question 8.21:

Two heavy spheres each of mass and radius are placed apart on a horizontal table. What is the gravitational force and potential at the mid point of the line joining the centers of the spheres?

Is an object placed at that point in equilibrium? If so, is the equilibrium stable or unstable?

The gravitational force at the mid point of the line joining the centers of the spheres: Zero

The potential at the mid point of the line joining the centers of the spheres

Is an object placed at that point in equilibrium: Yes;

And,

Is the equilibrium unstable.

Explanation:

The situation is represented in the given figure:

Mass of each sphere,

Separation between the spheres,

is the mid point between the spheres. Gravitational force at point will be zero. This is because gravitational force exerted by each sphere will act in opposite directions. Gravitational potential at point :

Any object placed at point will be in equilibrium state, but the equilibrium is unstable. This is because any change in the position of the object will change the effective force in that direction.

Question 8.22:

As you have learnt in the text, a geostationary satellite orbits the earth at a height of nearly from the surface of the earth. What is the potential due to earth’s gravity at the site of this satellite? (Take the potential energy at infinity to be zero). Mass of the earth,

Mass of the Earth,

Height of a geostationary satellite from the surface of the Earth,

Gravitational potential energy due to Earth’s gravity at height

Question 8.23:

A star the mass of the sun and collapsed to a size of rotates with a speed of . (Extremely compact stars of this kind are known as neutron stars. Certain stellar objects called pulsars belong to this category). Will an object placed on its equator remain stuck to its surface due to gravity? (Mass of the sun ).

Explanation:

A body gets stuck to the surface of a star if the inward gravitational force is greater than the outward centrifugal force caused by the rotation of the star.

Gravitational force,

Where,

Mass of the star

Mass of the body