Gravitation Tes...

A planet in a distant solar system is $$10$$ times more massive than the earth and its radius is $$10$$ times smaller. Given that the escape velocity from the earth is $$11 km$$ $$\mathrm{s}^{-1}$$, the escape velocity from the surface ofthe planet would be

The mass of a spaceship is $$1000\  kg$$. It is to be launched from the earths surface out into free space. The value of $$g$$ and $$R$$ (radius of earth) are $$10\  m/s$$ and $$6400\ km$$ respectively. The required energy for this work will be :

The height at which the acceleration due to gravity becomes $$\displaystyle \frac{\mathrm{g}}{9}$$ (where $$\mathrm{g}=$$ the acceleration due to gravity on the surface of the earth) in terms of $$\mathrm{R}$$, the radius of the earth, is: 

If g is the acceleration due to gravity on the earth's surface, the gain in the potential energy of an object of mass m raised from the surface of the earth to a height equal to the radius R of the earth, is:

What is the minimum energy required to launch a satellite of mass $$m$$ from the surface of a planet of mass $$M$$ and radius $$R$$ in a circular orbit at an altitude of $$2R$$?

 lf $$\mathrm{W}_{1},\ \mathrm{W}_{2}$$ and $$\mathrm{W}_{3}$$ represent the work done in moving a particle from A to $$\mathrm{B}$$ along three different paths 1, 2 and 3 respectively (as shown) in the gravitational field of a point mass $$\mathrm{m}$$, find the correct relation between $$\mathrm{W}_{1},\ \mathrm{W}_{2}$$ and $$\mathrm{W}_{3}$$.

A body weighs $$72 N$$ on the surface of the earth. What is the gravitational force on it due to the earth at a height equal to half the radius of the earth?

A body of mass '$$m$$' taken from the earth's surface to the height equal to twice the radius ($$R$$) of the earth. The change in potential energy of body will be

A body weighs 200 N on the surface of the earth. How much it weigh half way down to the centre of the earth ?

The ratio of escape velocity at earth$$(v_e)$$ to the escape velocity at a planet$$(v_p)$$ whose radius and mean density are twice as that of earth is: