Two identical solid copper spheres of radius R were placed in contact with each other. The gravitational attraction between them is proportional to:

1. $R^2$                                               

2. $R$

3. $R^4$                                               

4. $R^5$

     Which of the following statements is true? 

1.  g is less at the earth's surface than at a height above it or a depth below it

2.  g is the same at all places on the surface of the earth

3.  g has its maximum value at the equator

4.  g is greater at the poles than at the equator

A spring balance is graduated on sea level. If a body is weighed with this balance at

consecutively increasing heights from earth's surface, the weight indicated by the

balance 

1. Will go on increasing continuously

2. Will go on decreasing continuously

3. Will remain same

4. Will first increase and then decrease

The gravitational field due to a mass distribution is $E=K/x^3$ in the x-direction. (K is a

constant). Taking the gravitational potential to be zero at infinity, its value at a distance x

is

1. K/x                    

2. K/2x

3. $K/x^2$                 

4. K/2$x^2$

The change in the potential energy, when a body of mass \(m\) is raised to a height \(nR\) from the Earth's surface is: (\(R\) = Radius of the Earth)
1. \(mgR\left(\frac{n}{n-1}\right)\)
2. \(nmgR\)
3. \(mgR\left(\frac{n^2}{n^2+1}\right)\)
4. \(mgR\left(\frac{n}{n+1}\right)\)

The value of g on the earth's surface is 980 cm/$se{c}^2$ . Its value at a height of 64 km from

the earth's surface is

1.   $960.40 cm/se{c}^2$       

2.   $984.90 cm/se{c}^2$

3.   $982.45 cm/se{c}^2$         

4. 980.45 cm/$se{c}^2$

(Radius of the earth R = 6400 kilometers)     

If the earth suddenly shrinks (without changing mass) to half of its present radius, the acceleration due to gravity will be:

1. g/2                             

2. 4g

3. g/4                            

4. 2g

The masses and radii of the earth and moon are $M_{1, }{R}_1$ and $M_2, R_2$ respectively. Their centres are distance d apart. The minimum velocity with which a particle of mass m should be projected from a point midway between their centres so that it escapes to infinity is:

1. $2\sqrt{\frac{G}{D}\left(M_1+M_2\right)}$                 

2. $2\sqrt{\frac{2G}{D}(M_1+M_2)}$

3. $2\sqrt{\frac{GM}{D}\left(M_1+M_2\right)}$               

4. $2\sqrt{\frac{GM\left(M_1+M_2\right)}{D\left(R_1+R_2\right)}}$

If the mass of the earth is M, the radius is R and the gravitational constant is G, then work done to take

1 kg mass from earth surface to infinity will be:

1.  $\sqrt{\frac{GM}{2R}}$                      

2. $\frac{GM}{R}$

3.   $\sqrt{\frac{2GM}{R}}$                

4.   $\frac{GM}{2R}$

If $v_e$ and $v_o$ represent the escape velocity and orbital velocity of a satellite corresponding

to a circular orbit of radius R, then 

1. $v_e=v_o$                     

2. $\sqrt{2}{v}_o=v_e$

3. $v_e=v_o/\sqrt{2}$               

4. $v_e$ and $v_o$ are not related