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

A planet moving along an elliptical orbit is closest to the sun at a distance ${\mathrm{r}}_1$ and farthest away at a distance of ${\mathrm{r}}_2$. If ${\mathrm{v}}_1 \mathrm{and} {\mathrm{v}}_2$ are the linear velocities at these points respectively, then the ratio $\frac{{\mathrm{v}}_1}{{\mathrm{v}}_2}$ is:

(1)  ${\mathrm{r}}_2/{\mathrm{r}}_1$                                   

(2)   $({\mathrm{r}}_2/{\mathrm{r}}_1{)}^2$

(3)  ${\mathrm{r}}_1/{\mathrm{r}}_2$                                     

(4)   $({\mathrm{r}}_1/{\mathrm{r}}_2{)}^2$

A body projected vertically from the earth reaches a height equal to earth's radius before returning to the earth. The power exerted by the gravitational force is greatest:

(1) at the instant just before the body hits the earth

(2) it remains constant all through

(3) at the instant just after the body is projected

(4) at the highest position of the body  

A particle of mass m is thrown upwards from the surface of the earth with a velocity u. The mass and the radius of the earth are, respectively, M and R. G is gravitational constant and g is acceleration due to gravity on the surface of the earth. The minimum value of u so that the particle does not return back to earth is

(1) $\sqrt{\frac{2GM}{R}}$                                       

(2) $\sqrt{\frac{2GM}{R^{\mathit{2}}}}$

(3) $\sqrt{2g{R}^{\mathit{2}}}$                                       

(4) $\sqrt{\frac{2GM}{R^3}}$

The radii of the circular orbits of two satellites A and B of the earth are \(4R\) and \(R,\) respectively. If the speed of satellite A is \(3v,\) then the speed of satellite B will be:

A particle of mass M is situated at the centre of a spherical shell of mass M and radius a.The gravitational potential at a point situated at a/2 distance from the centre will be 

1. $-\frac{3GM}{a}$                                       2. $-\frac{2GM}{a}$

3. $-\frac{GM}{a}$                                         4. $-\frac{4GM}{a}$