Two bodies of masses m and 4m are placed at a distance r. The gravitational potential at a point on the line joining them where the gravitational field is zero is

1.  $-\frac{5\mathrm{Gm}}{\mathrm{r}}$

2.  $-\frac{6\mathrm{Gm}}{\mathrm{r}}$

3.  $-\frac{9\mathrm{Gm}}{\mathrm{r}}$

4.  0

3 particles each of mass m are kept at vertices of an equilateral triangle of side L. The

gravitational field at centre due to these particles is

1. zero                                                                       

2. $\frac{3GM}{L^2}$

3. $\frac{9GM}{L^2}$                                                                     

4. $\frac{12}{\sqrt{3}}\frac{GM}{L^2}$

The mass of the moon is $7.34\times {10}^{22}kg$ and the radius is $1.74\times {10}^{6}m$. The value of

gravitation field will be

1. $1.45 N/kg$                               

2. $1.55 N/kg$

3. $1.75 N/kg$                               

4.  $1.62 N/kg$

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

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

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

1.		2.
3.		4.

Dependence of intensity of gravitational field \((\mathrm{E})\) of the earth with distance \((\mathrm{r})\) from the centre of the earth is correctly represented by: (where \(\mathrm{R}\) is the radius of the earth)

1.		2.
3.		4.

A planet whose density is double of earth and radius is half of the earth, will produce gravitational field on its
surface:(\(g=\) acceleration due to gravity at the surface of earth)
1. \(g\)
2. \(2g\)
3. \(\frac{g}{2}\)
4. \(3g\)