Gravitation CBSE Questions & Answers

Titania, the largest moon of the planet Uranus, has \({1 \over 8}\) the radius of the earth and \({1 \over {1700}}\) the mass of the earth. What is the acceleration due to gravity at the surface of Titania? Data: G = 6.67\( \times \)\({\rm{1}}{0^{ - {\rm{11}}}}\) N m\(^{\rm{2}}\)/kg\(^{\rm{2}}\), RE = 6.38 \( \times \) \({\rm{1}}{0^{\rm{6}}}\) m, \({{\rm{m}}_{\rm{E}}}\) = 5.97 \( \times \) \({\rm{1}}{0^{{\rm{24}}}}\) kg

Titania, the largest moon of the planet Uranus, has \({1 \over 8}\) the radius of the earth and \({1 \over {1700}}\) the mass of the earth. What is the average density of Titania? Data: G = 6.67\( \times \)\({\rm{1}}{0^{ - {\rm{11}}}}\) N m\(^{\rm{2}}\)/kg\(^{\rm{2}}\), RE = 6.38 \( \times \) \({\rm{1}}{0^{\rm{6}}}\) m, \({{\rm{m}}_{\rm{E}}}\) = 5.97 \( \times \) \({\rm{1}}{0^{{\rm{24}}}}\)kg

A rocket is fired from the earth towards the sun. At what distance from the earth’s centre is the gravitational force on the rocket zero? Mass of the sun = 2 \( \times \) \({\rm{1}}{0^{{\rm{3}}0}}\) kg, mass of the earth = 6\( \times \) \({\rm{1}}{0^{{\rm{24}}}}\) kg. Neglect the effect of other planets etc. (orbital radius = 1.5 \( \times \) 1011 m).

How will you ‘weigh the sun’, that is estimate its mass? The mean orbital radius of the earth around the sun is 1.5 \( \times \) \({\rm{1}}{0^{\rm{8}}}\) km.

A Saturn year is 29.5 times the earth year. How far is the Saturn from the sun if the earth is 1.50 \( \times \) \({\rm{1}}{0^{\rm{8}}}\) km away from the sun?

A body weighs 63 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?

Assuming the earth to be a sphere of uniform mass density, how much would a body weigh half way down to the centre of the earth if it weighed 250 N on the surface?

A rocket is fired vertically with a speed of 5 km \({{\rm{s}}^{ - {\rm{1}}}}\) from the earth’s surface. How far from the earth does the rocket go before returning to the earth? Mass of the earth= 6.0 \( \times \) \({\rm{1}}{0^{{\rm{24}}}}\)kg; mean radius of the earth = 6.4 \( \times \) \({\rm{1}}{0^{\rm{6}}}\) m; G = 6.67 \( \times \) 10\(^{-{\rm{11}}}\) N m2 kg\(^{-{\rm{2}}}\).

The escape speed of a projectile on the earth’s surface is 11.2 km \({{\rm{s}}^{ - {\rm{1}}}}\). A body is projected out with thrice this speed. What is the speed of the body far away from the earth? Ignore the presence of the sun and other planets.

A satellite orbits the earth at a height of 400 km above the surface. How much energy must be expended to rocket the satellite out of the earth’s gravitational influence? Mass of the satellite = 200 kg; mass of the earth = 6.0 \( \times \) \({\rm{1}}{0^{{\rm{24}}}}\) kg; radius of the earth = 6.4 \( \times \) \({\rm{1}}{0^{\rm{6}}}\) m; G = 6.67 \( \times \) 10\(^{-{\rm{11}}}\) N m2 kg\(^{-{\rm{2}}}\).

For a satellite to be in a circular orbit 780 km above the surface of the earth, what orbital speed must it be given?

For a satellite to be in a circular orbit 780 km above the surface of the earth, what is the period of the orbit (in hours)?

Two satellites are in circular orbits around a planet that has radius 9.00 \( \times \) \({\rm{1}}{0^{\rm{6}}}\) m . One satellite has mass 68.0 kg, orbital radius 5.00 \( \times \) \({\rm{1}}{0^{\rm{7}}}\) m, and orbital speed 4800 m s. The second satellite has mass 84.0 kg and orbital radius 3.00 \( \times \) \({\rm{1}}{0^{\rm{7}}}\) m. What is the orbital speed of this second satellite?

Deimos, a moon of Mars, is about 12 km in diameter with mass 2.0 \( \times \) \({\rm{1}}{0^{{\rm{15}}}}\) kg. Suppose you are stranded alone on Deimos and want to play a one-person game of baseball. You would be the pitcher, and you would be the batter! With what speed would you have to throw a baseball so that it would go into a circular orbit just above the surface and return to you so you could hit it?

Deimos, a moon of Mars, is about 12 km in diameter with mass 2.0 \( \times \) \({\rm{1}}{0^{{\rm{15}}}}\) kg. Suppose you are stranded alone on Deimos and want to play a one-person game of baseball. You would be the pitcher, and you would be the batter! You have to throw a baseball so that it would go into a circular orbit just above the surface and return to you so you could hit it. How long (in hours) after throwing the ball should you be ready to hit it?