A satellite of mass $m$ is at a distance $a$ from $a$ star of mass $M$. The speed of satellite is $u$. Suppose the law of universal gravity is $F =  – G\frac{{Mm}}{{{r^{2.1}}}}$  instead of $F =  – G\frac{{Mm}}{{{r^2}}}$, find the speed of the statellite when it is at $a$ distance $b$ from the star.

If potential energy of a body of mass $m$ on the surface of earth is taken as zero then its potential energy at height $h$ above the surface of earth is [ $R$ is radius of earth and $M$ is mass of earth]

If the acceleration due to gravity at earth is $'g'$ and mass of earth is $80$ times that of moon and radius of earth is $4$ times that of moon, the value of acceleration due to gravity at the surface of moon will be

Masses and radii of earth and moon are $M_1,\, M_2$ and $R_1,\, R_2$ respectively. The distance between their centre is $'d'$ . The minimum velocity given to mass $'M'$ from the mid point of line joining their centre so that it will escape

Radius of the earth is $R$. If a body is taken to a height $3R$ from the surface of the earth than change in potential energy will be