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13
MCQ (Multiple Correct Answer)

There have been suggestions that the value of the gravitational constant $$G$$ becomes smaller when considered over very large time period (in billions of years) in the future. If that happens, for 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 sufficiently long time we will leave the solar system
14
MCQ (Multiple Correct Answer)

Supposing Newton's law of gravitation for gravitation forces $$\mathbf{F}_1$$ and $$\mathbf{F}_2$$ between two masses $$m_1$$ and $$m_2$$ at positions $$\mathbf{r}_1$$ and $$\mathbf{r}_2$$ read

$$\mathbf{F}_1=-\mathbf{F}_2=-\frac{\mathbf{r}_{12}}{r_{12}^3} \mathrm{GM}^2 0\left(\frac{m_1 m_2}{M_0^2}\right)^n$$

where $$M_0$$ is a constant of dimension of mass, $$\mathbf{r}_{12}=\mathbf{r}_1-\mathbf{r}_2$$ and $$n$$ is a number. In such a case,

A
the acceleration due to gravity on the earth will be different for different objects
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 in water
15
MCQ (Multiple Correct Answer)

Which of the following are true?

A
A polar satellite goes around the earth's pole in north-south direction
B
A geostationary satellite goes around the earth in east-west direction
C
A geostationary satellite goes around the earth in west-east direction
D
A polar satellite goes around the earth in east-west direction
16
MCQ (Multiple Correct Answer)

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
17
Subjective

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.

Explanation

Air molecules in the atmosphere are attracted vertically downward by gravitational force of the earth just like an apple falling from a tree. Air molecules move randomly due to their thermal velocity and hence the resultant motion of air molecules is not exactly in the vertical downward direction.

But in case of apple, only vertical motion dominates because of being heavier than air molecules. But due to gravity, the density of atmosphere increases near to the earth's surface.