# NCERT Class 11 Physics Solutions: Chapter 8 – Gravitation-Part 6

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Question 8.15:

A body weighs on the surface of the earth. What is the gravitational force on it due to the earth at a height equal to half the radius of the earth?

Weight of the body,

Acceleration due to gravity at height from the Earth’s surface is given by the relation:

Weight of a body of mass at height is given as:

Question 8.16:

Assuming the earth to be a sphere of uniform mass density, how much would a body weigh half way down to the centre of the earth if it weighed on the surface?

Weight of a body of mass m at the Earth’s surface,

Body of mass m is located at depth,

Where,

Acceleration due to gravity at depth is given by the relation:

Weight of the body at depth

Question 8.17:

A rocket is fired vertically with a speed of from the earth’s surface. How far from the earth does the rocket go before returning to the earth? Mass of the earth mean radius of the earth

from the centre of the Earth

Velocity of the rocket,

Mass of the Earth,

Height reached by rocket mass,

At the surface of the Earth,

Total energy of the rocket Kinetic energy Potential energy

At highest point

And potential energy

Total energy of the rocket

From the law of conservation of energy, we have

Total energy of the rocket at the Earth’s surface Total energy at height

Where, (Acceleration due to gravity on the earth’s surface)

Height achieved by the rocket with respect to the centre of the Earth