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2
MCQ (Single Correct Answer)

As observed from the earth, the sun appears to move in an approximate circular orbit. For the motion of another planet like mercury as observed from the earth, this would

A
be similarly true
B
not be true because the force between the earth and mercury is not inverse square law
C
not be true because the major gravitational force on mercury is due to the sun
D
not be true because mercury is influenced by forces other than gravitational forces
3
MCQ (Single Correct Answer)

Different points in the earth are at slightly different distances from the sun and hence experience different forces due to gravitation. For a rigid body, we know that if various forces act at various points in it, the resultant motion is as if a net force acts on the CM (centre of mass) causing translation and a net torque at the CM causing rotation around an axis through the CM. For the earth-sun system (approximating the earth as a uniform density sphere).

A
the torque is zero
B
the torque causes the earth to spin
C
the rigid body result is not applicable since the earth is not even approximately a rigid body
D
the torque causes the earth to move around the sun
4
MCQ (Single Correct Answer)

Satellites orbitting the earth have finite life and sometimes debris of satellites fall to the earth. This is because

A
the solar cells and batteries in satellites run out
B
 the laws of gravitation predict a trajectory spiralling inwards
C
of viscous forces causing the speed of satellite and hence height to gradually decrease
D
of collisions with other satellites
5
MCQ (Single Correct Answer)

Both the earth and the moon are subject to the gravitational force of the sun. As observed from the sun, the orbit of the moon

A
will be elliptical
B
will not be strictly elliptical because the total gravitational force on it is not central
C
is not elliptical but will necessarily be a closed curve
D
deviates considerably from being elliptical due to influence of planets other than the earth
6
MCQ (Single Correct Answer)

In our solar system, the inter-planetary region has chunks of matter (much smaller in size compared to planets) called asteroids. They

A
will not move around the sun, since they have very small masses compared to the sun
B
will move in an irregular way because of their small masses and will drift away into outer space
C
will move around the sun in closed orbits but not obey Kepler's laws
D
will move in orbits like planets and obey Kepler's laws
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