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 l2. of gravitation predict a trajectory spiralling inwards.awst |
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 . 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.
The following are the given statements:
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)