The speed with which the earth would have to rotate about its axis so that a person on the equator would weigh $\dfrac{3}{5}$th as much as at present is ($g$ = gravitational acceleration, $R$ = equatorial radius of the earth.)

A body of mass m is taken from earth surface to a height h equal to twice the radius of earth, the increase in potential energy will be ($g$ = acceleration due to gravity on earth's surface) (R - radius of earth)

The time taken by simple pendulum for one oscillation is T on earth's surface. Its time period becomes xT when taken to a height R (equal to earth's radius) above the earth's surface. The value of x is

The masses and radii of the earth and moon are $M_1$, $R_1$ and $M_2$, $R_2$ and respectively, Their centres are at a distance 'd' apart. The minimum speed with which body of mass 'm' should be projected from a distance $2d/3$ from the centre of $M_1$ so as to escape to infinity is