Gravitation · JEE Main previous year questions

A particle of mass $10\mathrm{g}$ is kept on the surface of a uniform sphere of mass $100\mathrm{kg}$ and radius $10\mathrm{cm}$. Find the work to be done against the gravitational force between them to take the particle far away from the sphere (you may take $G=6.67\times 10^{-11}\mathrm{N}{\mathrm{m}}^2/k{\mathrm{g}}^2$)

1. A.$3.33\times 10^{-10}\mathrm{J}$
2. B.$13.34\times 10^{-10}\mathrm{J}$
3. C.$6.67\times 10^{-10}\mathrm{J}$
4. D.$6.67\times 10^{-9}\mathrm{J}$

A satellite of mass $m$ revolves around the earth of radius $R$ at a height $x$ from its surface. If $g$ is the acceleration due to gravity on the surface of the earth, the orbital speed of the satellite is

1. A.$\frac{g{R}^2}{R+x}$
2. B.$\frac{gR}{R-x}$
3. C.$gx$
4. D.${\left(\frac{g{R}^2}{R+x}\right)}^{1/2}$

The time period of an earth satellite in circular orbit is independent of

1. A.both the mass and radius of the orbit
2. B.radius of its orbit
3. C.the mass of the satellite
4. D.neither the mass of the satellite nor the radius of its orbit

Suppose the gravitational force varies inversely as the $n^{th}$ power of distance. Then the time period of a planet in circular orbit of radius $R$ around the sun will be proportional to

1. A.$R^n$
2. B.$R^{\left(\frac{n-1}{2}\right)}$
3. C.$R^{\left(\frac{n+1}{2}\right)}$
4. D.$R^{\left(\frac{n-2}{2}\right)}$

If suddenly the gravitational force of attraction between Earth and a satellite revolving around it becomes zero, then the satellite will

1. A.continue to move in its orbit with same velocity
2. B.move tangentially to the original orbit with the same velocity
3. C.become stationary in its orbit
4. D.move towards the earth

The escape velocity of a body depends upon mass as

1. A.$m^0$
2. B.$m^1$
3. C.$m^2$
4. D.$m^3$