A launching vehicle carrying an artificial satellite of mass m is set for launch on the surface of the earth of mass M and radius R. If the satellite is intended to move in a circular orbit of radius 7R, the minimum energy required to be spent by the launching vehicle on the satellite is (Gravitational constant= G)

• $\frac{\mathrm{GMm}}{\mathrm{R}}$

• $- \frac{13 \mathrm{G} \mathrm{M} \mathrm{m}}{14 \mathrm{R}}$

• $\frac{\mathrm{GMm}}{7\mathrm{R}}$

• $-\frac{\mathrm{G} \mathrm{M} \mathrm{m}}{14 \mathrm{R}}$

This question contains Statement -1 and Statement-2. Of the four choices given after the statements, choose the one that best describes the two statements.
Statement – I:
For a mass M kept at the centre of a cube of side ‘a’, the flux of gravitational field passing through its sides is 4π GM.
and
Statement – II
If the direction of a field due to a point source is radial and its dependence on the distance ‘r’ for the source is given as 1/r₂, its flux through a closed surface depends only on the strength of the source enclosed by the surface and not on the size or shape of the surface

If g_E and g_m are the accelerations due to gravity on the surfaces of the earth and the moon respectively and if Millikan’s oil drop experiment could be performed on the two surfaces, one will find the ratio (electronic charge on the moon/ electronic charge on the earth) to be

A solid sphere is rotating in free space. If the radius of the sphere is increased keeping mass same which one of the following will not be affected?