Mass M is divided into two parts xM and $\left(1-x\right)M$ . For a given separation, the value of x

for which the gravitational attraction between the two pieces becomes maximum is

1. $\frac{1}{2}$                                 

2. $\frac{3}{5}$

3. 1                                   

4. 2

If earth is supposed to be a sphere of radius R, if $g_{30°}$ is value of acceleration due to gravity at latitude of 30^o and g at the pole, the value of $g-g_{{30}^o}$ is

1. $\frac{1}{4} {\omega }^{2}R$                      

2. $\frac{3}{4}{\omega }^{2}R$

3. ${\omega }^{2}R$                           

4. $\frac{1}{2}{\omega }^{2}R$

If M the mass of the earth and R its radius, the ratio of the gravitational acceleration and

the gravitational constant is

1. $\frac{R^2}{M}$                       

2. $\frac{M}{R^2}$

3. $M{R}^2$                       

4. $\frac{M}{R}$

Two sphere of mass m and M are situated in air and the gravitational force between them

is F. The space around the masses is now filled with a liquid of specific gravity 3. The

gravitational force will now be

1. F                                        

2. $\frac{F}{3}$  

3. $\frac{F}{9}$                                      

4. 3 F

Earth binds the atmosphere because of:

1. Gravity                                     

2. Oxygen between earth and atmosphere

3. Both 1 and 2

4 None of these

The mass of the earth is 81 times that of the moon and the radius of the earth is 3.5

times that of the moon. The ratio of the acceleration due to gravity at the surface of the

moon to that at the surface of the earth is

1. 0.15           

2. 0.0

3. 1             

4. 6

Spot the wrong statement :

The acceleration due to gravity ‘g’ decreases if

1. We go down from the surface of the earth towards its centre

2. We go up from the surface of the earth

3. We go from the equator towards the poles on the surface of the earth

4. The rotational velocity of the earth is increased

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