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qUESTIONS

The mass and radius of the earth and moon are M1, R1 and M2, R2 respectively. Their centres are at a distance ‘d’ apart. The minimum speed with which a body of mass ‘m’ should be projected from a distance 2d/3 from the centre of M1, so as to escape to ∞ is:

If the distance between the sun and the earth is increased 3 times, then attraction between sun and earth will:

A body is projected vertically upwards from earth’s surface. If its kinetic energy of projection is equal to half of its minimum value required to escape from earth’s gravitational influence then the height upto which it rises is: (R = radius of earth)

The mass and radius of earth is Me and Re respectively and that of moon is Mm, and Rm respectively. The distance between the centre of earth and that of moon is ‘D’. The minimum speed required for a body (mass ‘m’) to project from a point midway between their centers to escape to infinity is:

A body of mass ‘m’ is dropped from a height R/2 from earth’s surface where R is the radius of earth. Its speed when it will hit the earth’s surface is: (V= escape velocity from earth’s surface)

Consider earth to be a sphere of radius R rotating about its own axis with angular speed w ‘ge’ and ‘gp’ are the accelerations due to gravity at the equator and the poles respectively, then (gp – ge) is given by:

The escape velocity for a planet whose mass is six times the mass of earth and radius is twice the radius of earth will be. (V= escape velocity from the earth)

A geostationary satellite is revolving around the earth. If the radius of the earth is ‘R’ and the angular speed about its own axis is ‘w’ then, the radius of the orbit of the geostationary satellite is:

At what height from the earth’s surface, the gravitational potential and the value of gravitational acceleration are 5.4 x 10^7 J/kg^2 and 6.0 m/s^2 respectively? (Radius of earth = 6400 km)

If ‘T is the length of a day of earth, ‘M’ and ‘R’ are the mass and radius of the earth respectively, then the height of a geostationary satellite is: [G= Universal gravitational constant]

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