NCERT Class 11 Physics Solutions: Chapter 8 – Gravitation-Part 7

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Question 8.18:

The escape speed of a projectile on the earth’s surface is . A body is projected out with thrice this speed. What is the speed of the body far away from the earth? Ignore the presence of the sun and other planets.

Escape velocity of a projectile from the Earth,

Projection velocity of the projectile,

Velocity of the projectile far away from the Earth

Total energy of the projectile on the Earth

Gravitational potential energy of the projectile far away from the Earth is zero.

Total energy of the projectile far away from the Earth

From the law of conservation of energy, we have

Question 8.19:

A satellite orbits the earth at a height of above the surface. How much energy must be expended to rocket the satellite out of the earth’s gravitational influence? Mass of the satellite ; mass of the earth ; radius of the earth ;

Mass of the Earth,

Mass of the satellite,

Universal gravitational constant,

Height of the satellite,

Total energy of the satellite at height

Orbital velocity of the satellite,

Total energy of height,

The negative sign indicates that the satellite is bound to the Earth. This is called bound energy of the satellite.

Energy required to send the satellite out of its orbit Bound energy

Question 8.20:

Two stars each of one solar mass are approaching each other for a head on collision. When they are a distance , their speeds are negligible. What is the speed with which they collide? The radius of each star is . Assume the stars to remain undistorted until they collide. (Use the known value of ).

Mass of each star,

Distance between the stars,

For negligible speeds, total energy of two stars separated at distance

Now, consider the case when the stars are about to collide:

Velocity of the stars

Distance between the centers of the stars

Total kinetic energy of both stars

Total potential energy of both stars

Total energy of the two stars

Using the law of conservation of energy, we can write: