Escape velocity of a body of 1 kg mass on a planet is 100 m/sec. Gravitational Potential energy of the body at the planet is -

(1)   – 5000 J                     

(2)  – 1000 J

(3)   – 2400 J                      

(4)  5000 J

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?

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 -

(a) $1.99\times {10}^{30}kg$                        (b) $7.56\times {10}^{22}kg$

 (c) $5.98\times {10}^{24}kg$                       (d) $7.65\times {10}^{22}kg$

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 -

(a) 1 km/sec                          (b) 4 km/sec

(c) 8 km/sec                          (d) 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