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Question (1)

QN0035473

The earth is an approximate sphere. If the interior contained matter which is not of the same density everywhere, then on the surface of the earth, the acceleration due to gravity

(A)
will be directed towards the centre but not the same everywhere
(B)
will have the same value everywhere but not directed towards the centre
(C)
will be same everywhere in magnitude directed towards the centre
(D)
cannot be zero at any point

Correct Answer: D

Explanation:

Let the density of earth as a sphere is uniform, then it can be treated as point mass placed at its centre then acceleration due to gravity , at the centre. But if the density of earth is considered as a sphere of non-uniform then value of ' ' will be different at different points

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Question (2)

QN0035474

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 force

Correct Answer: C

Explanation:

Force of attraction between any two objects obeys the inverse square law.
As observed from the earth, the sun appears to move in an approximate circular orbit. The gravitational force of attraction between the earth and the sun always follows inverse square law.

Due to relative motion between the earth and mercury, the orbit of mercury, as observed from the earth will not be approximately circular, since the major gravitational force on mercury is due to the sun is very large than due to earth and due to the relative motion to sun and earth with mercury. (a) As we know that, the torque on earth due to gravitational attractive force on earth is zero:

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Question (3)

QN0035475

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 (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

Correct Answer: A

Explanation:

As the earth is revolving around the sun in a circular motion due to gravitational attraction. The force of attraction will be of radial nature i.e., angle between position vector and force is also, zero.

So, torque

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Question (4)

QN0035476

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

Correct Answer: C

Explanation:

As the total (P.E.) of the earth satellite orbiting in orbit is negative , where is radius of the satellite and is mass of the earth.

Due to the viscous force acting on satellite, energy decreases continuously and radius of the orbit or height decreases gradually.

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Question (5)

QN0035477

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

Correct Answer: B

Explanation:

The major force acting on moon is due to gravitational force of attraction by sun and earth and moon is not always in line of joining sun and earth.

As observed from the sun, two types of forces are acting on the moon one is due to gravitational attraction between the sun and the moon and the other is due to gravitational attraction between the earth and the moon. So these two force have different lines of action and it will not be strictly elliptical because total force on the moon is not central.

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Question (6)

QN0035478

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

Correct Answer: D

Explanation:

Asteroids are also being acted upon by central gravitational forces, hence Asteroid will move in circular orbits like planets and obey Kepler's laws.

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Question (7)

QN0035479

Choose the wrong option.

(A)
Inertial mass is a measure of difficulty of accelerating a body by an external force whereas the gravitational mass is relevant in determining the gravitational force on it by an external mass
(B)
That the gravitational mass and inertial mass are equal is an experimental result
(C)
That the acceleration due to gravity on the earth is the same for all bodies is due to the equality of gravitational mass and inertial mass
(D)
Gravitational mass of a particle like proton can depend on the presence of neighbouring heavy objects but the inertial mass cannot

Correct Answer: D

Explanation:

Gravitational mass of proton is equivalent to its inertial mass and is independent of presence of neighbouring heavy objects so verifies the option (d).

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Question (8)

QN0035480

Particles of masses and are respectively at points and with is much-much smaller than and at time , they are all at rest as given in figure. At subsequent times before any collision takes place.

(A)
will remain at rest
(B)
will move towards
(C)
will move towards
(D)
will have oscillatory motion

Correct Answer: C

Explanation:

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Question (1)

The earth is an approximate sphere. If the interior contained matter which is not of the same density everywhere, then on the surface of the earth, the acceleration due to gravity

Explanation:

Link:

Question (2)

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

Explanation:

Link:

Question (3)

Explanation:

Link:

Question (4)

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

Explanation:

Link:

Question (5)

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

Explanation:

Link:

Question (6)

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

Explanation:

Link:

Question (7)

Choose the wrong option.

Explanation:

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Question (8)

Particles of masses and are respectively at points and with is much-much smaller than and at time , they are all at rest as given in figure. At subsequent times before any collision takes place.

Explanation:

Link:

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