Gravitation Physics - Gravitation

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

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 influence of planets other than 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 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.

If the law of gravitation, instead of being inversesquare law, becomes an inversecube law.

1. Planets will not have elliptic orbits.
2. Circular orbits of planets is not possible.
3. Projectile motion of a stone thrown by hand on the surface of the earth will be approximately parabolic.
4. There will be no gravitational force inside a spherical shell of uniform density.

Which of the following options are correct?

1. Acceleration due to gravity decreases with increasing altitude.
2. Acceleration due to gravity increases with increasing depth (assume the earth to be a sphere of uniform density).
3. Acceleration due to gravity increases with increasing latitude.
4. Acceleration due to gravity is independent of the mass of the earth.

Particles of masses 2M, m and M are respectively at points A, B and C with AB = ½ (BC). m is muchmuch smaller than M and at time t = 0, they are all at rest.

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 gravitational force between a hollow spherical shell (of radius R and uniform density) and a point mass is F. Show the nature of F vs r graph where r is the distance of the point from the centre of the hollow spherical shell of uniform density.

What is the angle between the equatorial plane and the orbital plane of Polar satel lite?

What is the angle between the equatorial plane and the orbital plane of Geostationary satel lite?

How is the gravitational force between two point masses affected when they are dipped in water keeping the separation between them the same?

An astronaut inside a small spaceship orbiting around the earth cannot detect gravity. If the space station orbiting around the earth has a large size, can he hope to detect gravity?

We can shield a charge from electric fields by putting it inside a hollow conductor. Can we shield a body from the gravitational influence of nearby matter by putting it inside a hollow sphere or by some other means?

Shown are several curves. Explain with reason, which ones amongst them can be possible trajectories traced by a projectile (neglect air friction).

Give one example each of central force and non - central force.

What is the direction of areal velocity of the earth around the sun?

Out of aphelion and perihelion, where is the speed of the earth more and why?

Molecules in air in the atmosphere are attracted by gravitational force of the earth. Explain why all of them do not fall into the earth just like an apple falling from a tree.

Draw areal velocity versus time graph for mars.

A mass m is placed at P a distance h along the normal through the centre O of a thin circular ring of mass M and radius r

If the mass is removed further away such that OP becomes 2h, by what factor the force of gravitation will decrease, if h = r?

An object of mass m is raised from the surface of the earth to a height equal to the radius of the earth, that is, taken from a distance R to 2R from the centre of the earth. What is the gain in its potential energy?

Mean solar day is the time interval between two successive noon when sun passes through zenith point (meridian). Sidereal day is the time interval between two successive transit of a distant star through the zenith point (meridian). By drawing appropriate diagram showing earth’s spin and orbital motion, show that mean solar day is four minutes longer than the sidereal day. In other words, distant stars would rise 4 minutes early every successive day.

A satellite is in an elliptic orbit around the earth with aphelion of 6R and perihelion of 2R where R = 6400km is the radius of the earth. Find eccentricity of the orbit. Find the velocity of the satellite at apogee and perigee. What should be done if this satellite has to be transferred to a circular orbit of radius 6R?

[G = 6.67 × 10^–11 SI units and M = 6 × 10²⁴kg]

Show the nature of the following graph for a satellite orbiting the earth.

1. KE vs orbital radius R
2. PE vs orbital radius R
3. TE vs orbital radius R.