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Choose the correct statement from the following :
The weightlessness of an astronaut moving in a satellite is a situation of :
1. zero g
2. no gravity
3. zero mass
4. free fall

A satellite is moving around the earth with a speed v in a circular orbit of radius r. If the orbital radius is decreased by 1%, the speed of the satellite will :
1. increase by 1 %
2. increase by 0.5 %
3. decrease by 1 %
4. decrease by 0.5 %

If the moon is to escape from the gravitational field of the earth forever, it will require a velocity :
1. 11.2 km/s
2. less than 11.2 km/s
3. slightly more than 11.2 km/s
4. 22.4 km/s

The kinetic energy required to make a body move to infinity from the earth's surface is :
1. infinite
2. 2 mgR
3. $\frac{1}{2}mgR$
4. mgR

${\mathrm{V}}_{\mathrm{e}}$ and ${\mathrm{V}}_{\mathrm{p}}$ denotes the escape velocity from the earth and another planet having twice the radius and the same mean density as the earth. Then :
1. ${\mathrm{V}}_{\mathrm{e}}={\mathrm{V}}_{\mathrm{p}}$
2. ${\mathrm{V}}_{\mathrm{e}}={\mathrm{V}}_{\mathrm{p}}/2$
3. ${\mathrm{V}}_{\mathrm{e}}=2{\mathrm{V}}_{\mathrm{p}}$
4. ${\mathrm{V}}_{\mathrm{e}}={\mathrm{V}}_{\mathrm{p}}/4$

The earth moves around the sun in an elliptical orbit as shown in the fig. The ratio $\frac{OA}{OB}=x$. The ratio of the speed of the earth at B and at A is :

1. $\sqrt{\mathrm{x}}$
2. x
3. ${\mathrm{x}}^2$
4. $\mathrm{x}\sqrt{2}$

What is the height at which the weight of the body will be the same as at the same depth from the surface of the earth? The radius of the earth is R.
1. $\frac{\mathrm{R}}{2}$
2. $\sqrt{5}R-R$
3. $\frac{\sqrt{\mathit{5}}\mathit{R}\mathit{-}\mathit{R}}{\mathit{2}}$
4. $\frac{\sqrt{3}R\mathit{-}R}{\mathit{2}}$

Two equal masses m and m are hung from a balance whose scale pan differs in vertical height by h/2. The error in weighing in terms of density of the earth $\mathrm{\rho }$ is :
1. $\frac{1}{3}\mathrm{\pi }<mspace\; width="1em"></mspace>\mathrm{G\rho }<mspace\; width="1em"></mspace>\mathrm{mh}$
2. $\mathrm{\pi }<mspace\; width="1em"></mspace>\mathrm{G\rho }<mspace\; width="1em"></mspace>\mathrm{mh}$
3. $\frac{4}{3}\mathrm{\pi }<mspace\; width="1em"></mspace>\mathrm{G\rho }<mspace\; width="1em"></mspace>\mathrm{mh}$
4. $\frac{8}{3}\mathrm{G\rho }<mspace\; width="1em"></mspace>\mathrm{mh}$

Imagine a light planet revolving around a very massive star in a circular orbit of radius R with a period of revolution T. If the gravitational force of attraction between the planet and the star is proportional to ${\mathrm{R}}^{-3/2}$, then ${\mathrm{T}}^2$ is proportional to :
1. ${\mathrm{R}}^3$
2. ${\mathrm{R}}^{5/2}$
3. ${\mathrm{R}}^{3/2}$
4. ${\mathrm{R}}^{7/2}$

Select the proper graph between the gravitational potential $\left({\mathrm{V}}_{\mathrm{g}}\right)$ due to the hollow sphere and distance (r) from its centre.
1. 
2. 
3. 
4. 

The figure shows the motion of a planet around the sun in an elliptical orbit with the sun at the focus. The shaded areas A and B are also shown in the fig. which can be assumed to be equal. If ${\mathrm{t}}_1$ and ${\mathrm{t}}_2$ represent the time taken by the planet to move from a to b and c to d respectively, then

1. ${\mathrm{t}}_1<{\mathrm{t}}_2$
2. ${\mathrm{t}}_1>{\mathrm{t}}_2$
3. ${\mathrm{t}}_1={\mathrm{t}}_2$
4. from the given information relation between ${\mathrm{t}}_1$ and ${\mathrm{t}}_2$ cannot be determined

The gravitational field in a region is given by $\overrightarrow{\mathrm{E}}=\left(2\hat{i}+3\hat{j}\right)$ N/kg. No work is done by the gravitational field when a particle is moved on the line 3y+kx = 5. The value of k should be :
1. 1
2. 2
3. 3
4. 4

The gravitational field in a region is given by $\overrightarrow{\mathrm{I}}=\left(5\hat{i}+12\hat{j}\right)<mspace\; width="1em"></mspace>N<mspace\; width="1em"></mspace>k{g}^{-1}$. The magnitude of the gravitational force acting on a particle of mass 2 kg placed at origin will be :
1. 13 N
2. 26 N
3. 39 N
4. 17 N

Three particles each of mass m are placed at A, C, and D, where AB = BC = BD = a. The net gravitational force on the particle at D is :

1. $\frac{{\mathrm{Gm}}^2}{{\mathrm{a}}^2}<mspace\; width="1em"></mspace>along<mspace\; width="1em"></mspace>AC$
2. $\frac{\sqrt{2}{\mathrm{Gm}}^2}{{\mathrm{a}}^2}<mspace\; width="1em"></mspace>along<mspace\; width="1em"></mspace>\mathrm{DB}$
3. $\frac{{\mathrm{Gm}}^2}{\sqrt{2}{\mathrm{a}}^2}<mspace\; width="1em"></mspace>along<mspace\; width="1em"></mspace>\mathrm{BD}$
4. $\frac{{\mathrm{Gm}}^2}{\sqrt{2}{\mathrm{a}}^2}<mspace\; width="1em"></mspace>along<mspace\; width="1em"></mspace>\mathrm{DB}$