Question with Solution

A meteorite moving radially inwards towards a planet of mass M, collides perfectly inelastically with a space station orbiting in a circuit orbit of radius R. Mass of the space station is 10 times of the meteorite. The combined body moves in a new orbit which has minimum distance R/2 from the center of planet. The velocity u of the meteorite before the collision is given by $\mathrm{N}\sqrt{\frac{29\mathrm{GM}}{2\mathrm{R}}}$. Fill N in your OMR sheet.

\[

$$\sqrt{\frac{29\mathrm{GM}}{2\mathrm{R}}}$$

\]