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10
MCQ (Multiple Correct Answer)

If the law of gravitation, instead of being inverse square law, becomes an inverse cube law

A
planets will not have elliptic orbits
B
circular orbits of planets is not possible
C
projectile motion of a stone thrown by hand on the surface of the earth will be approximately parabolic
D
there will be no gravitational force inside a spherical shell of uniform density
11
MCQ (Multiple Correct Answer)
 

If the mass of the sun were ten times smaller and gravitational constant $$G$$ were ten times larger in magnitude. Then,

A
walking on ground would become more difficult
B
the acceleration due to gravity on the earth will not change
C
raindrops will fall much faster
D
airplanes will have to travel much faster
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
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