In an elliptical orbit under gravitational force, in general

(1) Tangential velocity is constant

(2) Angular velocity is constant

(3) Radial velocity is constant

(4) Areal velocity is constant

Earth is revolving around the sun, if the distance of the Earth from the Sun is reduced to 1/4^th of the present distance then the present year length reduced to -

(1)$\frac{1}{4}$                                        

(2)$\frac{1}{2}$  

(3)$\frac{1}{8}$                                        

(4)$\frac{1}{6}$  

Two satellite are revolving around the earth with velocities $v_1$ and $v_2$ and in radii $r_1$ and $r_2\left(r_1>r_2\right)$respectively. Then -

(1)$v_1=v_2$                                

(2)$v_1>v_2$  

(3)$v_1<v_2$                                

(4)$\frac{v_1}{r_1}=\frac{v_2}{r_2}$  

If orbital velocity of planet is given by $v=G^a{M}^b{R}^c$, then -

(1)$a=1/3, b=1/3, c=‐1/3$      

(2)$a=1/2, b=1/2, c=‐1/2$      

(3)$a=1/2, b=‐1/2, c=1/2$   

(4)$a=1/2, b=‐1/2, c=‐1/2$          

The mass of a planet that has a moon whose time period and orbital radius are T and R respectively can be written as -

(1)$4{\mathrm{\pi }}^2{\mathrm{R}}^3{\mathrm{G}}^{‐1}{\mathrm{T}}^{‐2}$                                

(2)$8{\mathrm{\pi }}^2{\mathrm{R}}^3{\mathrm{G}}^{‐1}{\mathrm{T}}^{‐2}$  

(3)$12{\mathrm{\pi }}^2{\mathrm{R}}^3{\mathrm{G}}^{‐1}{\mathrm{T}}^{‐2}$                               

(4)$16{\mathrm{\pi }}^2{\mathrm{R}}^3{\mathrm{G}}^{‐1}{\mathrm{T}}^{‐2}$  

The eccentricity of earth's orbit is 0.0167. The ratio of its maximum speed in its orbit to its minimum speed is

(a)   2.507                                             (b)   1.033

(c)   8.324                                             (d)   1.000

Assuming the earth to have a constant density, point out which of the following curves show the variation of acceleration due to gravity from the centre of earth to the points far away from the surface of earth -

The radius of orbit of a planet is two times that of the earth. The time period of the planet is:

(1)   4.2 years                          

(2)   2.8 years

(3)   5.6 years                          

(4)   8.4 years

The diagram showing the variation of gravitational potential of earth with distance r from the centre of earth is -