Questions in Gravitation

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If M the mass of the earth and R its radius, the ratio of the gravitational acceleration and the gravitational constant is
A body of mass m rises to height h = R/5 from the earth's surface, where R is earth's radius. If g is acceleration due to gravity at earth's surface, the increase in potential energy is
In a gravitational field, at a point where the gravitational potential is zero
The gravitational field due to a mass distribution is $E = K/{x^3}$ in the x-direction. (K is a constant). Taking the gravitational potential to be zero at infinity, its value at a distance x is
The mass of the earth is $6.00 imes {10^{24}}\,kg$ and that of the moon is $7.40 \times {10^{22}}\,kg$. The constant of gravitation $G = 6.67 \times {10^{ - 11}}\,N - {m^2}/k{g^2}$. The potential energy of the system is $ - 7.79 \times {10^{28}}\,joules$. The mean distance between the earth and moon is
The change in potential energy, when a body of mass m is raised to a height nR from the earth's surface is (R = Radius of earth)
The masses and radii of the earth and moon are ${M_1},\,{R_1}$ and ${M_2},\,{R_2}$ respectively. Their centres are distance d apart. The minimum velocity with which a particle of mass m should be projected from a point midway between their centres so that it escapes to infinity is
If mass of earth is M, radius is R and gravitational constant is G, then work done to take 1 kg mass from earth surface to infinity will be
A rocket is launched with velocity 10 km/s. If radius of earth is R, then maximum height attained by it will be [RPET 1997]
There are two bodies of masses 100 kg and 10000 kg separated by a distance 1 m. At what distance from the smaller body, the intensity of gravitational field will be zero

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