Question 6: The ratio of acceleration due to gravity at a depth h below the surface of earth and at a height h above the surface for h < < radius of earth:
Answer: (b) increases linearly with h
Explanation: Let R be ratius of earth and g the acceleartion due to gravity on earth's surface. Then the desired ratio (say x) is:
(h < < R)
From this expression we see that x increase linearly with h.
Question 7: Figure shows the variatiuon of energy with the orbit radius r of a satellite in a circular motion. Mark the correct statement.
Answer: (c) A and B are the kinetic and potential energies respectively and C the total energy of the satellite
Explanation: Kinetic energy
Potential energy
and the total energy
Kinetic energy is always positive and
Potential energy is negative and
Similarly, total energy is also negative and Also | E | < | PE |
Therefore, A is kinetic energy, B is potential energy and C is total energy of the satellite.
Question 8: Rate of change of weight near the earth's surface varies with heigt (h) as:
Answer: (b) h 0
Question 9: A satellite of mass m moves along an elliptical path around the earth. The areal velocity of the satellite is proportional to:
Answer: (c) m0
Explanation: Areal velocity = constant
Here, L = mvr sinq (angular momentum)
i.e.,
Question 10: The angular momentum (L) of earth revolving round the sun is proportional to rn, where r isthe orbital radius of the earth. The value of n is : (assume the orbit to be circular)
Answer: (a)
Explanation:: L = mvr ...(i)
...(ii)
From Eqs. (i) and (ii), we can see that
L = m (GMr)1/2
or
But
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