Assuming the earth to have a constant density, point out which of the following curves show the variation of acceleration due to gravity from the centre of earth to the points far away from the surface of earth -

The radius of orbit of a planet is two times that of the earth. The time period of the planet is:

(1)   4.2 years                          

(2)   2.8 years

(3)   5.6 years                          

(4)   8.4 years

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 -