The ratio of escape velocity at earth $\left(v_e\right)$ to the escape velocity at a planet $\left(v_p\right)$ whose radius and mean density are twice that of the earth is

(a) $1:2\sqrt{2}$                    (b)$1:4$

(c) $1:\sqrt{2}$                      (d) $1:2$

Kepler's third law states that the square of the period of revolution (T) of a planet around the sun, is proportional to the third power of the average distance r between the sun and planet i.e. T²=Kr^3, here K is constant. If the masses of the sun and planet are M and m respectively, then as per Newton's law of gravitation, the force of attraction between them is F=GMm/r², here G is gravitational constant. The relation between G and K is described as

(1) GK=4π² 

(2) GMK=4π²
 

(3) K=G
 

(4) K=l/G
 

Two spherical bodies of masses M and 5M and radii R and 2R are released in free space with initial separation between their centres equal to 12R. If they attract each other due to gravitational force only, then the distance covered by the smaller body before collision is

(1)2.5 R

(2)4.5 R

(3)7.5 R

(4)1.5 R

A remote sensing satellite of the earth revolves in a circular orbit at a height of \(0.25\times 10^{6}\) m above the surface of the earth. If the earth’s radius is \(6.38\times 10^{6}\) m and \(g = 9.8\) ms^-1, then the orbital speed of the satellite is:
1. \(7.76\) kms^-1
2. \(8.56\) kms^-1
3. \(9.13\) kms^-1
4. \(6.67\) kms^-1

A satellite S is moving in an elliptical orbit around the earth. The mass of the satellite is very small as compared to the mass of the earth. Then,

(1) the angular momentum of S about the centre of the earth changes in direction, but its magnitude remains constant

(2) the total mechanical energy of S varies periodically with time

(3) the linear momentum of S remains constant in magnitude

(4) the acceleration of S is always directed towards the centre of the earth

A black hole is an object whose gravitational field is so strong that even light cannot escape from it. To what approximate radius, would earth (mass=5.98X 10²⁴ kg) have to be compressed to be a black hole?

(1) 10^-9m 

(2) 10^-6 m

(3) 10^-2 m

(4) 100 m

Dependence of intensity of gravitational field (E) of earth with distance (r) from centre of earth is correctly represented by 

1.		2.
3.		4.

A body of mass m is taken from the earth’s surface to the height equal to twice the radius (R) of the earth. The change in potential energy of the body will be
\(1.~2mgR\)
\(2.~\frac{2}{3}mgR\)
\(3.~3mgR\)
\(4.~\frac{1}{3}mgR\)




 

Infinite number of bodies, each of mass 2 kg are situated on x-axis at distance 1m, 2m,  4m, 8m, respectively from the origin. The resulting gravitational potential due to this system at the origin will be

(a)-G

(b)-8/3G

(c)-4/3G

(d)-4G

The height at which the weight of a body becomes 1/16th, its weight on the surface of the earth (radius R), is:

(1) 5R                                 

(2) 15R

(3) 3R                                 

(4) 4R