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NCERT Class 11 Physics Solutions: Chapter 8 – Gravitation-Part 6
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?
Answer:
Weight of the body,
Acceleration due to gravity at height from the Earths 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?
Answer:
Weight of a body of mass m at the Earth՚s surface,
Body of mass m is located at depth,
Where,
Radius of the Earth
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 earths surface. How far from the earth does the rocket go before returning to the earth? Mass of the earth mean radius of the earth
Answer:
from the centre of the Earth
Velocity of the rocket,
Mass of the Earth,
Radius 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 earths surface)
Height achieved by the rocket with respect to the centre of the Earth