The diagram showing the variation of gravitational potential of earth with distance r from the centre of earth is -

The condition for a uniform spherical mass m of radius r to be a black hole is [G= gravitational constant and g= acceleration due to gravity] .

(1) ${\left(2Gm/r\right)}^{1/2}\le c$                

(2) ${\left(2Gm/r\right)}^{1/2}=c$ 

(3) ${\left(2Gm/r\right)}^{1/2}\ge c$                

(4)  ${\left(gm/r\right)}^{1/2}\ge c$

A sphere of mass M and radius R₂ has a concentric cavity of radius R₁ as shown in figure. The force F exerted by the sphere on a particle of mass m located at a distance r from the centre of sphere varies as $(0\le \mathrm{r}\le \infty )$. 

Which one of the following graphs represents correctly the variation of the gravitational field (I) with the distance (r) from the centre of a spherical shell of mass M and radius a ?

Suppose, the acceleration due to gravity at the earth’s surface is 10 $\mathrm{m}/{\mathrm{s}}^2$ and at the surface of Mars, it is 4.0 $\mathrm{m}/{\mathrm{s}}^2$. A 60 kg passenger goes from the earth to Mars in a spaceship moving with a constant velocity. Neglect all other objects in the sky. Which part of the figure best represents the weight (net gravitational force) of the passenger as a function of time ?

(a) A                              (b) B

(c) C                              (d) D

Which of the following graphs represents the motion of a planet moving about the sun ?

The correct graph representing the variation of total energy (${\mathrm{E}}_{\mathrm{t}}$), kinetic energy (${\mathrm{E}}_{\mathrm{k}}$) and potential energy (U) of a satellite with its distance from the centre of the earth is -

What is the intensity of gravitational field of the centre of a spherical shell?

(1)     $Gm/r^2$           

(2)    g

(3)      Zero             

(4)    None of these

The diameters of two planets are in the ratio 4 : 1 and their mean densities in the ratio 1 : 2. The acceleration due to gravity on the planets will be in the ratio of:

1. 1 : 2                           
2. 2 : 3
3. 2 : 1                      
4. 4 : 1