Gravitation

MCQs(Part - II)

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:

is constant
increases linearly with h
increases parabolically with h
decreases

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.

C shows the total energy, B the kinetic energy and A the potential energy of the satellite.
A shows the kinetic energy, B the total energy and C the potential energy of the satellite
A and B are the kinetic and potential energies respectively and C the total energy of the satellite
C and A are the kinetic and potential energies respectively and B the total energy of the satellite

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:

h
h ⁰
h^-1
h^1/2

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:

m
m^{- 1}
m⁰
m^1/2

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

But