Gravitation CBSE Questions & Answers

Two stars each of one solar mass (= 2 \( \times \) \({\rm{1}}{0^{{\rm{3}}0}}\) kg) are approaching each other for a head on collision. When they are a distance \({\rm{1}}{0^{\rm{9}}}\) km, their speeds are negligible. What is the speed with which they collide? The radius of each star is 104 km. assume the stars to remain undistorted until they collide. (Use the known value of G)

Two heavy spheres each of mass 100 kg and radius 0.10 m are placed 1.0 m apart on a horizontal table. What is the gravitational force and potential at the mid point of the line joining the centers of the spheres? Is an object placed at that point in equilibrium? If so, is the equilibrium stable or unstable?

A geostationary satellite orbits the earth at a height of nearly 36,000 km from the surface of the earth. What is the potential due to earth’s gravity at the site of this satellite? (Take the potential energy at infinity to be zero).Mass of the earth = 6.0\( \times \) \({\rm{1}}{0^{{\rm{24}}}}\)kg, radius = 6400 km.

A spaceship is stationed on Mars. How much energy must be expended on the spaceship to launch it out of the solar system? Mass of the space ship = 1000 kg; mass of the sun = 2 \( \times \) \({\rm{1}}{0^{{\rm{3}}0}}\) kg; mass of mars = 6.4 \( \times \) \({\rm{1}}{0^{{\rm{23}}}}\) kg; radius of mars = 3395 km; radius of the orbit of mars = 2.28 \( \times \) \({\rm{1}}{0^{\rm{8}}}\) km; G = 6.67 \( \times \) \({\rm{1}}{0^{ - {\rm{11}}}}\) N m2 kg\(^{-{\rm{2}}}\).

A rocket is fired ‘vertically’ from the surface of mars with a speed of 2 km \({{\rm{s}}^{-{\rm{1}}}}\) . If 20 percent of its initial energy is lost due to Martian atmospheric resistance, how far will the rocket go from the surface of mars before returning to it? Mass of mars = 6.4 \( \times \) \({\rm{1}}{0^{{\rm{23}}}}\) kg; radius of mars = 3395 km; G = 6.67 \( \times \) \({\rm{1}}{0^{ - {\rm{11}}}}\) N \({{\rm{m}}^{\rm{2}}}\) kg\(^{-{\rm{2}}}\).

The star Cancri is 57 light-years from the earth and has a mass 0.85 times that of our sun. A planet has been detected in a circular orbit around Cancri with an orbital radius equal to 0.11 times the radius of the earth’s orbit around the sun. What is the orbital speed? The mean orbital radius of the earth around the sun is 1.5 \( \times \) \({\rm{1}}{0^{\rm{8}}}\) km.

The star Cancri is 57 light-years from the earth and has a mass 0.85 times that of our sun. A planet has been detected in a circular orbit around Cancri with an orbital radius equal to 0.11 times the radius of the earth’s orbit around the sun. What is the orbital period of the planet of Cancri? The mean orbital radius of the earth around the sun is 1.5 \( \times \) \({\rm{1}}{0^{\rm{8}}}\) km

On October 15, 2001, a planet was discovered orbiting around the star HD 68988. Its orbital distance was measured to be 10.5 million kilometers from the center of the star, and its orbital period was estimated at 6.3 days. What is the mass of HD 68988?

A uniform, solid, 1000.0-kg sphere has a radius of 5.00 m. Find the gravitational force this sphere exerts on a 2.00-kg point mass placed at a distance of 5.01 m from the center of the sphere

A uniform, solid, 1000.0-kg sphere has a radius of 5.00 m. Find the gravitational force this sphere exerts on a 2.00-kg point mass placed at a distance of 2.50 m from the center of the sphere

The acceleration due to gravity at the North Pole of Neptune is approximately 10.7 \( \times \) m/ \({{\rm{s}}^{\rm{2}}}\). Neptune has mass 1.0 \( \times \) \({\rm{1}}{0^{{\rm{26}}}}\) kg and radius 2.5 \( \times \) \({\rm{1}}{0^{\rm{4}}}\) km and rotates once around its axis in about 16 h. What is the gravitational force on a 5.0-kg object at the north pole of Neptune?

The acceleration due to gravity at the North Pole of Neptune is approximately 10.7 \( \times \) \({\rm{m}}/{{\rm{s}}^{\rm{2}}}\). Neptune has mass 1.0 \( \times \) \({\rm{1}}{0^{{\rm{26}}}}\) kg and radius 2.5 \( \times \) \({\rm{1}}{0^{\rm{4}}}\) km and rotates once around its axis in about 16 h. What is the apparent weight a 5.0-kg object at Neptune’s equator?

Neutron stars, such as the one at the center of the Crab Nebula, have about the same mass as our sun but have a much smaller diameter. If you weigh 675 N on the earth, what would you weigh at the surface of a neutron star that has the same mass as our sun and a diameter of 20 km?

Moon has a mass of 7.36 \( \times \) \({\rm{1}}{0^{{\rm{22}}}}\) kg, and a radius of 1.74 \( \times \) \({\rm{1}}{0^{\rm{6}}}\) m. Calculate the acceleration due to gravity on the moon.

The space shuttle releases a 470-kg communications satellite while in an orbit that is 280 km above the surface of the Earth. A rocket engine on the satellite boosts it into a geosynchronous orbit, which is an orbit in which the satellite stays directly over a single location on the Earth. How much energy did the engine have to provide?