1. State Newton's Universal Law of Gravitation.

Every body in the universe attracts every other body with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. This force of attraction between any two bodies in the universe known as the gravitation is mutual and acts along the line joining the centres of the two bodies.

If m₁ and m₂ are the masses of two particles separated by a distance r, the force of attraction between them is given by   where G is called the Universal Gravitational Constant.

If m₁ = m₂ = 1 and r = 1, then G = F. Hence gravitational constant is numerically equal to the force of attraction between two unit masses separated by unit distance.

2. What are the properties of gravitational force?

(1)It is always attractive in nature.

(2)It is independent of the intervening medium.

(3)It is an action - reaction pair.

(4)It is two body interaction that is, gravitational force between two bodies is independent of the presence or absence of other bodies.

(5)Gravitational force is central as it acts along the line joining the centres of the two bodies.

(6) Gravitational force is conservative.

(7)It holds good over a wide range of distances. It is found to be true from inter - planetary distance to inter - atomic distance.

(8)It obeys inverse square law.

3. Define Acceleration due to gravity(g).

The uniform acceleration produced on a freely falling body due to the gravitational pull of the earth is known as the acceleration due to gravity.

Let us consider the earth to be a perfect sphere of mass M and radius R. Consider a body of mass m placed on the surface of the earth. Assuming the mass of the earth is concentrated at its centre, the force of gravity or the weight of the body is given by

Thus g is independent of the mass m of the body. Acceleration due to gravity at a point on the surface of the earth is the gravitational force of attraction on a unit mass at that point.

4. What do you meant by Geo stationary satellite (Synchronous satellites)?

These are artificial satellites orbiting the earth with a period similar (synchronous) to that of the earth. The orbit in which geostationary satellites are staying is called parking orbit or geo stationary orbit.They move in the same direction of rotation as that of the earth that is from west to east and with the same angular velocity as that of the earth. Relative velocity of a geostationary satellite with respect to the earth is zero. It appears stationary with respect to a particular position on the surface of the earth.

Such satellites are used for the purpose of communication. Radio, TV and telephone signals from a station on the earth are directed to a satellite and the satellite retransmits them to some other stations on the earth. In this way range of communication can be increased. Accurate and precise weather forecasting can be made with the help of artificial satellites.

5.What are the uses of polar satellites?

They are used to collect data

(i)for ground water supply

(ii)for detecting the areas under forest

(iii)for preparing waste land maps

(iv)for the assessment of drought

(v)for the assessment of crop diseases

(vi)for identifying the sources of pollution

(vii)for detecting the potential fishing zones

(viii)to locate the position and movement of the troops of enemy that is for spying purpose

(ix) To locate the place and time for any nuclear explosion etc.

6. State Kepler's laws of planetary motion.

(1)The orbit of a planet relative to the sun is an ellipse with the sun at one of its foci and lies in a plane containing the sun. This is called the law of orbit.

(2)The radius vector from the sun to the planet sweeps out equal areas in equal intervals of time. That is areal velocity of a planet is a constant. This is called law of areas.

(3)The square of the time period of revolution of a planet is directly proportional to the cube of its semi major axis.   T² α a³  The law is called the law of period.`

7.Two bodies of mass 10 kg and 25 kg are placed at a distance of 0.2 m apart. Find the force between them.Given that G = 6.67×10^-11 SI units.

8. A mass M is split into two parts m and (M - m) which are separated by a certain distance. What ratio m/M maximises the gravitational force between the parts?

If r is the distance between m and (M - m) the gravitational force will be

9. A rocket is fired towards the sun. At what point on the path is the gravitational force on the rocket zero. Mass of the sun = 2 x10³⁰ kg, Mass of the earth = 6 x10²⁴ kg, orbital radius =1.5 x 10¹¹m. Ignore the presence of other satellites.

Let x be the distance from the earth where gravitational force on the rocket is zero.

10.The acceleration due to gravity at the moon's surface is 1.67 ms^-2. If the radius of the moon is 1.74 ×10⁶ m, calculate the mass of the Moon. G = 6.67×10^-11 S.I. unit.

11. If the radius of the earth shrinks by 2%, mass remaining the same, then how would the acceleration due to gravity change?

Let M and R be the mass and radius of the earth. The acceleration due to gravity near the surface of the earth is given by,

12. A body weighs 63 N on the earth. What is the gravitational force on it at a height equal to half the radius of the earth?

13.The acceleration due to gravity on the moon's surface is 1.7 ms^-2. The radius of the moon is 0.27 times that of the earth. Acceleration due to gravity on the surface of the earth is 9.8 ms^-2. Find the ratio of the mass of the earth to that of the moon.

14.The escape velocity of a projectile on the earth's surface is 11.2 kms^-1. A body is projected with twice this speed. What is the speed of the body far away from the earth (infinity)? Ignore the presence of sun and other planets.

15. Period of Saturn is 29.5 years. Calculate the average distance of Saturn from the sun. (The radius of the earth's orbit is 1.5×10⁸km).

16. What is the difference between gravitation and gravity?

Gravitation is the force of attraction acting between any two bodies of the universe. On the other hand, the force of attraction between every body and earth is the earth's gravitational pull or gravity. Clearly, gravity is a special case of gravitation where one of the bodies is earth and the other body lying on earth or near the surface of earth. The following are the salient differences between gravitation and gravity:

(i) Gravitation is the force of attraction between any two bodies of the universe whereas gravity is the force of attraction exerted by earth on a body lying on or near the surface of earth.

(ii) The gravitational force between two masses m₁ and m₂ separated by a distance r is F = Gm₁m₂/r² where G is the Universal Gravitational Constant. On the other hand, force of gravity on a body of mass m is F = mg where g is acceleration due to gravity. Note that mg is called the weight of the body.

(iii)The force of gravitation between two bodies cannot be zero unless r→∞. However, force of gravity at the centre of earth is zero.

17. Which pulls with greater force on the oceans of the earth, the sun or moon?

The sun, but it is so distant that it attracts all parts of the earth with almost equal strength. Hence its effectiveness in raising tides is less than that of the moon.

18. Consider an apple at the top of a tree that is pulled by earth gravity with a force of 1 N. If the tree were twice as tall, would the force of gravity be only 1/4 as strong?

No, because the twice-as-tall tree is not twice as far from the earth's centre. The tree's height would have to be equal to the radius of the earth (6370 km) before the force on apple reduces to (1/4)N. Before its weight reduces by 1%, the apple or any object must be raised 32 km above the surface of earth- nearly four times the height of Mount Everest. So as a practical matter, we disregard the effects of everyday changes in elevation.