The depth at which the effective value of acceleration due to gravity is $\frac{g}{4}$, is:

1. R                              

2. $\frac{3R}{4}$

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

4. $\frac{R}{4}$

The value of \(g\) at a particular point is \(9.8~\text{m/s}^2\). Suppose the earth suddenly shrinks uniformly to half its present size without losing any mass then value of \(g\) at the same point will now become: (assuming that the distance of the point from the centre of the earth does not shrink)

The earth (mass = $6\times {10}^{24}kg$ ) revolves round the sun with angular velocity

$2\times {10}^{‐7}rad/s$ in a circular orbit of radius $1.5\times {10}^{8}km$ . The force exerted by the sun on

the earth in Newtons, is

1. $18\times {10}^{25}$                               

2. Zero

3. $27\times {10}^{39}$                               

4. $36\times {10}^{21}$

The gravitational force between two point masses $m_1$  and $m_2$  at separation r is given by $F=k\frac{m_1{m}_2}{r^2}$  The constant k                                                                

1. Depends on system of units only

2. Depends on medium between masses only

3. Depends on both 1 and 2

4. Is independent of both 1 and 2

The density of a newly discovered planet is twice that of earth. The acceleration due to

gravity at the surface of the planet is equal to that at the surface of the earth. If the

radius of the earth is R, the radius of the planet would be

1. 2R                   

2. 4R

3. $\frac{1}{4}R$               

4. $\frac{1}{2}R$     

If R is the radius of the earth and g the acceleration due to gravity on the earth's surface,

the mean density of the earth is:

1. $4\pi G/3gR$                                 

2. $3\pi R/4gG$

3. $3g/4\pi RG$                               

4.$\pi RG/12G$        

A planet has twice the radius but the mean density is $\frac{1}{4}th$ as compared to earth. What is the ratio of escape velocity from earth to that from the planet ?

1. 3:1                                                                 

2. 1:2

3. 1:1                                                                 

4. 2:1

A body weighs 500 N on the surface of the earth. How much would it weigh halfway

below the surface of the earth?

1. 125 N                               

2.  250 N

3. 500 N                               

4.  1000 N

Who among the following gave first the experimental value of G?

1. Cavendish                               

2. Copernicus

3. Brook Taylor                           

4. None of these