The maximum and minimum distances of a comet from the sun are $8\times {10}^{12}$ m and $1.6\times {10}^{12}$ m. If its velocity when nearest to the sun is 60 m/s, what will be its velocity in m/s when it is farthest -

(1) 12                                      

(2) 60

(3) 112                                     

(4) 6

A body revolved around the sun 27 times faster than the earth. What is the ratio of their radii?

(1)   1/3                                    

(2)   1/9

(3)   1/27                                  

(4)   1/4

The period of the moon’s rotation around the earth is nearly 29 days. If the moon’s mass were 2 fold, its present value and all other things remained unchanged, the period of the moon’s rotation would be nearly:

(1)$29\sqrt{2} days$                                       

(2)$29/\sqrt{2} days$

(3)$29\times 2 days$                                       

(4)29 days

If two planets are at mean distances $d_1$ and $d_2$ from the sun and their frequencies are n₁ and n₂ respectively, then:

1. ${n_1}^2{d_1}^2=n_2{d_2}^2$                                 

2. ${n_2}^2{d_2}^3={n_1}^2{d_1}^3$

3. $n_1{d_1}^2=n_2{d_2}^2$                                   

4. ${n_1}^2{d}_1={n_2}^2{d}_2$

Suppose the law of gravitational attraction suddenly changes and becomes an inverse cube law i.e., $F\propto 1/r^3$ but the force still remains a central force, then:

A planet is revolving around the sun as shown in an elliptical path.

The correct option is:

(1)   The time taken in travelling DAB is less than that for BCD

(2)   The time taken in travelling DAB is greater than that for BCD

(3)   The time taken in travelling CDA is less than that for ABC

(4)   The time taken in travelling CDA is greater than that for ABC

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)$a=1/2, b=‐1/2, c=‐1/2$