A satellite of mass $\frac{M}{2}$ is revolving around earth in a circular orbit at a height of $\frac{R}{3}$ from earth surface. The angular momentum of the satellite is $\mathrm{M} \sqrt{\frac{\mathrm{GMR}}{x}}$. The value of $x$ is _________ , where M and R are the mass and radius of earth, respectively. ( G is the gravitational constant)

If the radius of earth is reduced to three-fourth of its present value without change in its mass then value of duration of the day of earth will be ________ hours 30 minutes.

A simple pendulum is placed at a place where its distance from the earth's surface is equal to the radius of the earth. If the length of the string is $$4 m$$, then the time period of small oscillations will be __________ s. [take $$g=\pi^2 m s^{-2}$$]

If the earth suddenly shrinks to $$\frac{1}{64}$$th of its original volume with its mass remaining the same, the period of rotation of earth becomes $$\frac{24}{x}$$h. The value of x is __________.