At the surface of a certain planet, acceleration due to gravity is one-quarter of that on earth. If a brass ball is transported to this planet, then which one of the following statements is not correct?

1.	The mass of the brass ball on this planet is a quarter of its mass as measured on earth
2.	The weight of the brass ball on this planet is a quarter of the weight as measured on earth
3.	The brass ball has the same mass on the other planet as on earth
4.	The brass ball has the same volume on the other planet as on earth

Weight of 1 kg becomes 1/6 kg on moon. If radius of moon is $1.768\times {10}^{6}m$, then the mass of moon will be -

1. $1.99\times {10}^{30}kg$                        
2. $7.56\times {10}^{22}kg$
3. $5.98\times {10}^{24}kg$                       
4. $7.65\times {10}^{22}kg$

Let g be the acceleration due to gravity at earth's surface and K be the rotational kinetic energy of the earth. Suppose the earth's radius decreases by 2% keeping all other quantities same, then

1.  g decreases by 2% and K decreases by 4%

2.  g decreases by 4% and K increases by 2%

3.  g increases by 4% and K increases by 4%

4.  g decreases by 4% and K increases by 4%

The distance between centre of the earth and moon is 384000 km. If the mass of the earth is $6\times {10}^{24} kg$ and $G=6.66\times {10}^{-11} N{m}^2/k{g}^2$ . The speed of the moon is nearly -

1. 1 km/sec                         
2. 4 km/sec
3. 8 km/sec                         
4. 11.2 km/sec

A body is projected vertically upwards from the surface of a planet of radius \(R\) with a velocity equal to half the escape velocity for that planet. The maximum height attained by the body is:
1. \(\frac{R}{3}\)
2. \(\frac{R}{2}\)
3. \(\frac{R}{4}\)
4. \(\frac{R}{5}\)

A satellite is launched into a circular orbit of radius \(R\) around the Earth while a second satellite is launched into an orbit of radius \(1.02~\text{R}\). The percentage difference in the time periods of the two satellites is: 

Distance of geostationary satellite from the center of the Earth $(R_e=6400 km)$ in terms of $R_e$ is-

1. $13.76 R_e$                        

2. $10.76 R_e$

3. $6.59 R_e$                            

4. $2.56 R_e$

Energy required to move a body of mass m from an orbit of radius 2R to 3R is

1.    $GMm/12R^2$               

2.    $GMm/3R^2$

3.     $GMm/8R$                 

4.     $GMm/6R$

If the radius of the earth contracts by 2% and its mass remains the same, then weight of the body at the earth surface :

1.  Will decrease                      

2.  Will increase

3.  Will remain the same             

4.  None of these

The kinetic energy needed to project a body of mass m from the earth surface (radius R) to infinity is -

1.   mgR/2                 

2.  2 mgR

3.   mgR                   

4.   mgR/4