An artificial satellite of mass m moves in an orbit whose radius is n times the radius of earth. Assuming the resistance to the motion is proportional to square of velocity ie $F= av^2$ where a is a constant. How long will the satellite take to fall to earth. M-mass of earth R- radius of earth

Question

\[(a)\;\frac{m}{a} \bigg(\frac{R}{GM}\bigg)\sqrt {n-1} \quad (b)\;\frac{m}{a} \sqrt{\frac{R}{GM}}(\sqrt n -1) \quad (c)\;\frac{m}{a} \sqrt {\frac{RG}{M}}(\sqrt {n+1}) \quad (d)\;\frac{m}{a} \sqrt {\frac{RG}{M}}(\sqrt n-1) \]