Gravitation CBSE Questions & Answers

Calculate the escape speed from the Earth for a 5 000-kg spacecraft. 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 \( \times \) \({\rm{1}}{0^{-{\rm{11}}}}\) N m2 kg\(^{-{\rm{2}}}\).

Determine the kinetic energy a 5 000-kg spacecraft must have in order to escape the Earth’s gravitational field. 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 \( \times \) \({\rm{1}}{0^{-{\rm{11}}}}\) N m2 kg\(^{-{\rm{2}}}\)

The asteroid Toro has a radius of about 5.0 km. Assuming that the density of Toro is the same as that of the earth (5.5 g/cm3) find its total mass and find the acceleration due to gravity at its surface. 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 \( \times \) \({\rm{1}}{0^{-{\rm{11}}}}\) N m2 kg\(^{-{\rm{2}}}\)

The asteroid Toro has a radius of about 5.0 km. assuming that the density of Toro is the same as that of the earth (5.5 g/cm3) Suppose an object is to be placed in a circular orbit around Toro, with a radius just slightly larger than the asteroid’s radius. What is the speed of the object?. 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 \( \times \) \({\rm{1}}{0^{-{\rm{11}}}}\) N m2 kg\(^{-{\rm{2}}}\)

Calculate the percent difference between your weight in Sacramento, near sea level, and at the top of Mount Everest, which is 8800 m above sea level.

Consider a spacecraft in an elliptical orbit around the earth. At the low point, or perigee, of its orbit, it is 400 km above the earth’s surface; at the high point, or apogee, it is 4000 km above the earth’s surface. What is the period of the spacecraft’s orbit?

Consider a spacecraft in an elliptical orbit around the earth. At the low point, or perigee, of its orbit, it is 400 km above the earth’s surface; at the high point, or apogee, it is 4000 km above the earth’s surface. Using conservation of angular momentum, find the ratio of the spacecraft’s speed at perigee to its speed at apogee.

Consider a spacecraft in an elliptical orbit around the earth. At the low point, or perigee, of its orbit, it is 400 km above the earth’s surface; at the high point, or apogee, it is 4000 km above the earth’s surface. Using conservation of energy, find the speed at perigee and the speed at apogee.

Consider a spacecraft in an elliptical orbit around the earth. At the low point, or perigee, of its orbit, it is 400 km above the earth’s surface; at the high point, or apogee, it is 4000 km above the earth’s surface. Using conservation of energy, find the speed at perigee and the speed at apogee. It is necessary to have the spacecraft escape from the earth completely. If the spacecraft’s rockets are fired at perigee, by how much would the speed have to be increased to achieve this?

Consider a spacecraft in an elliptical orbit around the earth. At the low point, or perigee, of its orbit, it is 400 km above the earth’s surface; at the high point, or apogee, it is 4000 km above the earth’s surface. Using conservation of energy, find the speed at perigee and the speed at apogee. It is necessary to have the spacecraft escape from the earth completely. If the spacecraft’s rockets are fired at apogee, by how much would the speed have to be increased to achieve this?

A 5000-kg spacecraft is in a circular orbit 2000 km above the surface of Mars. How much work must the spacecraft engines perform to move the spacecraft to a circular orbit that is 4000 km above the surface?

Planets are not uniform inside. Normally, they are densest at the center and have decreasing density outward toward the surface. Model a spherically symmetric planet, with the same radius as the earth, as having a density that decreases linearly with distance from the center. Let the density be 15.0 \( \times \) 10\(^{\rm{3}}\)kg/m\(^{\rm{3}}\) at the center and 2.0 \( \times \) 10\(^{\rm{3}}\) kg/m3 at the surface. What is the acceleration due to gravity at the surface of this planet?

An object in the shape of a thin ring has radius 'a' and mass M. A uniform sphere with mass m and radius R is placed with its center at a distance x to the right of the center of the ring, along a line through the center of the ring, and perpendicular to its plane. What is the gravitational force that the sphere exerts on the ring-shaped object?

If a film of width l is stretched in the longitudinal direction a distance d by force F, surface tension is given by

Derive an expression for the work required to move an Earth satellite of mass m from a circular orbit of radius 2 \({{\rm{R}}_{\rm{E}}}\)to one of radius 3 \({{\rm{R}}_{\rm{E}}}\).