Chapter 8: Gravitation

If the mass of the sun were ten times smaller and gravitational constant G was ten times larger in magnitude

a) walking on the ground would become more difficult

b) the acceleration due to gravity on earth will not change

c) raindrops will fall much faster

d) aeroplanes will have to travel much faster

If the sun and the planets carried huge amounts of opposite charges,

a) all three of Kepler’s laws would still be valid

b) only the third law will be valid

c) the second law will not change

d) the first law will still be valid

There have been suggestions that the value of the gravitational constant G becomes smaller when considered over a very large time period in the future. If that happens to our earth,

a) nothing will change

b) we will become hotter after billions of years

c) we will be going around but not strictly in closed orbits

d) after a sufficiently long time, we will leave the solar system

Supposing Newton’s law of gravitation for gravitation forces F1 and F2 between two masses m1 and m2 at positions r1 and r2 read
where Mo is a constant of the dimension of mass, r₁₂ = r₁ – r₂ and n is a number. In such a case,

a) the acceleration due to gravity on earth will be different for different object

b) none of the three laws of Kepler will be valid

c) only the third law will become invalid

d) for n negative, an object lighter than water will sink into the water

Which of the following is true?

The centre of mass of an extended body on the surface of the earth and its centre of gravity

a) are always at the same point for any size of the body

b) are always at the same point only for spherical bodies

c) can never be at the same point

d) is close to each other for objects, say of sizes less than 100 m

e) both can change if the object is taken deep inside the earth

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

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

Draw areal velocity versus time graph for mars.

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