What is the source of centripetal force that a planet requires to revolve around the Sun? On what factors does that force depend?
Soln:
Gravitational force is the source of centripetal force required to revolve around the sun. This force depends on the distance between the planet and sun along with their masses. If this force becomes zero as a result of the absence of centripetal force, the planet would shift to moving tangentially outwards to the circular route.
17. On the earth, a stone is thrown from a height in a direction parallel to the earth’s surface while another stone is simultaneously dropped from the same height. Which stone would reach the ground first and why?
Soln:
Both the stones reach the ground simultaneously as they are dropped from the same height and their initial velocity will be the same.
18. Suppose gravity of earth suddenly becomes zero, then in which direction will the moon begin to move if no other celestial body affects it?
Soln:
If there is no gravitational pull from the earth, the moon starts to move in a straight line tangent to its circular path.
19. Identical packets are dropped from two aeroplanes, one above the equator and the other above the north pole, both at height h. Assuming all conditions are identical, will those packets take same time to reach the surface of earth. Justify your answer.
Soln:
The value of ‘g’ – acceleration due to gravity is constant, but depending upon the surface of the earth it varies from place to place as earth is not completely spherical. As it is flattened at the poles, the value of ‘g’ is maximum at the poles and the bulging at the equator causes the ‘g’ value to be minimum at the equator. The ‘g’ value increases as we move towards the poles. Hence, the packets falls gradually at the equator in comparison to the poles. Thereby, the packets stay in air for longer when dropped at the equator.
20. The weight of any person on the moon is about 1/6 times that on the earth. He can lift a mass of 15 kg on the earth. What will be the maximum mass, which can be lifted by the same force applied by the person on the moon?
Soln:
Weight of person on moon = 1/6th of weight on earth
Therefore, ‘g’ on moon = 1/6th ‘g’ on earth
The force that is applied by the man to lift mass ‘m’ is
F = mg = 15g (on earth)
If he can lift a certain mass ‘m’ by applying the same force on moon, then
F = 15*6=90kg
This proves acceleration due to gravity on the moon is 1/6th of acceleration due to gravity on earth. Hence the person can lift a mass 6 times heavier on moon than on earth.
21. Calculate the average density of the earth in terms of g, G and R.
Soln:
g= GM /R2
M=gR2/G
Density of earth D= mass/volume
=Gr2/GxVe
= gR2/G4πR/3
= 3g/4µGR
22. The earth is acted upon by gravitation of Sun, even though it does not fall into the Sun. Why?
Soln:
Sun provides enough centripetal force to keep the earth in its orbit and the earth provides centrifugal force due to its motion. These two forces balance each other which prevents the earth from falling into the sun.
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