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12
MCQ (Multiple Correct Answer)

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
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
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