Q. No.| 1. | will be directed towards the centre but not the same everywhere. |
| 2. | will have the same value everywhere but not directed towards the centre. |
| 3. | will be the same everywhere in magnitude directed towards the centre. |
| 4. | cannot be zero at any point. |
As observed from the earth, the sun appears to move in an approximately circular orbit. For the motion of another planet like mercury as observed from the earth, this would:
| 1. | be similarly true. |
| 2. | not be true because the force between the earth and mercury is not inverse square law. |
| 3. | not be true because the major gravitational force on mercury is due to the sun. |
| 4. | not be true because mercury is influenced by forces other than gravitational forces. |
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 net torque at the centre of mass causing rotation around an axis through the CM. For the earth-sun system (approximating the earth as a uniform density sphere):
| 1. | the torque is zero. |
| 2. | the torque causes the earth to spin. |
| 3. | the rigid body result is not applicable since the earth is not even approximately a rigid body. |
| 4. | the torque causes the earth to move around the sun. |
Satellites orbiting the earth have a finite life and sometimes debris of satellites fall to the earth. This is because:
| 1. | the solar cells and batteries in satellites run out. |
| 2. | the laws of gravitation predict a trajectory spiralling inwards. |
| 3. | of viscous forces causing the speed of the satellite and hence height to gradually decrease. |
| 4. | of collisions with other satellites. |
| 1. | will be elliptical. |
| 2. | will not be strictly elliptical because the total gravitational force on it is not central. |
| 3. | is not elliptical but will necessarily be a closed curve. |
| 4. | deviates considerably from being elliptical due to the influence of planets other than the earth. |
In our solar system, the interplanetary region has chunks of matter (much smaller in size compared to planets) called asteroids. They:
| 1. | will not move around the sun, since they have very small masses compared to the sun. |
| 2. | will move in an irregular way because of their small masses and will drift away into outer space. |
| 3. | will move around the sun in closed orbits but not obey Kepler’s laws. |
| 4. | will move in orbits like planets and obey Kepler’s laws. |
Choose the wrong option.
| 1. | Inertial mass is a measure of the difficulty of accelerating a body by an external force whereas gravitational mass is relevant in determining the gravitational force on it by an external mass. |
| 2. | That the gravitational mass and inertial mass are equal is an experimental result. |
| 3. | 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. |
| 4. | Gravitational mass of a particle-like proton can depend on the presence of neighbouring heavy objects but the inertial mass cannot. |
Particles of masses \(2M, m\) and \(M\) are respectively at points \(A, B\) and \(C\) with \(A B = \dfrac{1}{2} \left( B C \right).\) The mass \(m\) is much-much smaller than \(M\) and at time \(t = 0\), they are all at rest as given in the figure. At subsequent times before any collision takes place,
1. \(m\) will remain at rest.
2. \(m\) will move towards \(M.\)
3. \(m\) will move towards \(2M.\)
4. \(m\) will have oscillatory motion.
| (a) | Acceleration due to gravity decreases with increasing altitude. |
| (b) | Acceleration due to gravity increases with increasing depth (assume the earth to be a sphere of uniform density). |
| (c) | Acceleration due to gravity increases with increasing latitude. |
| (d) | Acceleration due to gravity is independent of the mass of the earth. |
Choose the correct alternatives:
| 1. | (b), (d) | 2. | (a), (c) |
| 3. | (c), (d) | 4. | (a), (c), (d) |
If the law of gravitation, instead of being inverse square law, becomes an inverse cube law:
| (a) | planets will not have elliptic orbits. |
| (b) | circular orbits of planets are not possible. |
| (c) | the projectile motion of a stone thrown by hand on the surface of the earth will be approximately parabolic. |
| (d) | there will be no gravitational force inside a spherical shell of uniform density. |
Choose the correct alternatives:
1. (a), (d)
2. (a), (c)
3. (c), (d)
4. (b), (d)
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