Class 11 NEET Physics Gravitation Questions

The satellite of mass $m$ is moving in a circular orbit of radius $r$. $\therefore$ Kinetic energy of the satellite, $K = \frac{G M m}{2 r}$ .....(i) Potential energy of the satellite, $U = \frac{-G M m}{r}$ ....(ii) Orbital speed of satellite, $v = \sqrt{\frac{G M}{r}}$ ....(iii) Time-period of satellite, $T = \left[\left( \frac{4 \pi^{2}}{G M} \right) r^{3} t\right]^{1/2}$ .....(iv) Given $m_{S_{1}} = 4 m_{S_{2}}$ since $M, r$ is same for both the satellites $S_{1}$ and $S_{2}$ $\therefore$ From equation (ii), we get $U \propto m$ $\therefore \frac{U_{S_{1}}}{U_{S_{2}}} = \frac{m_{S_{1}}}{m_{S_{2}}} = 4$ or, $U_{S_{1}} = 4 U_{S_{2}}$ Option (a) is wrong. From (iii), since $v$ is independent of the mass of a satellite, the orbital speed is same for both satellites $S_{1}$ and $S_{2}$ Hence option (b) is correct. From (i), we get $K \propto m$ $\therefore \frac{K_{S_{1}}}{K_{S_{2}}} = \frac{m_{S_{1}}}{m_{S_{2}}} = 4$ or, $K_{S_{1}} = 4 K_{S_{2}}$ Hence option (c) is wrong. From (iv), since $T$ is independent of the mass of a satellite, time period is same for both the satellites $S_{1}$ and $S_{2}.$ Hence option(d) is wrong.