B M Sharma Solutions for Chapter: Gravitation, Exercise 1: DPP 6.1

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

If the mass of the sun were ten times smaller than what it is and the gravitational constant $G$ were ten times larger in magnitude, then, 

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, 

Supposing Newton's law of gravitation for gravitation forces $F_1$and $F_2$between two masses $m_1$and $m_2$at positions $r_1$and $r_2$read

$F_1=-F_2=\frac{r_{12}}{r_{12}^3}G{M}_0^2{\left(\frac{m_1{m}_2}{M_0^2}\right)}^n$

where $M_0$is a constant of the dimension of mass, $r_{12}=r_1-r_2$and $n$is a number? In such a case 

The mean radius of the Earth's orbit around the Sun is $1.5\times {10}^{11} \mathrm{m}.$The mean radius of the orbit of Mercury around the Sun is $6\times {10}^{10} \mathrm{m}.$Find the time in the Mercury will rotate around the Sun.

Imagine a light planet revolving around a very massive star in a circular orbit of radius $R$ with a period of revolution $T$. If the gravitational force of attraction between planet and star is proportional to $R^{-\frac{5}{2}}$, then $T^2$ is proportional to

A planet moves around the sun. At a given point $P$, it is closest from the sun at a distance $d_1$ and has a speed $v_1$. At another point $Q$, when it is farthest from the sun at a distance $d_2$, its speed will be

Two planets revolve around the sun with frequencies $N_1$ and $N_2$ revolutions per year. If their average orbital radii be $R_1$ and $R_2$ respectively, then $\frac{R_1}{R_2}$ is equal to