Gravitation · JEE Main previous year questions

2012 2 questions

1. Q332012 · 26 May 2012 · Shift 1

   A satellite moving with velocity $v$ in a force free space collects stationary interplanetary dust at a rate of $\frac{dM}{dt}=\alpha v$ where $M$ is the mass (of satellite + dust) at that instant. The instantaneous acceleration of the satellite is

   1. A.$-\frac{\alpha v^2}{2M}$
   2. B.$-\frac{\alpha v^2}{M}$
   3. C.$-\alpha v^2$
   4. D.$-\frac{2\alpha v^2}{M}$
   Show answer

   Answer: B

2. Q382012 · 26 May 2012 · Shift 1

   A point particle is held on the axis of a ring of mass $m$ and radius $r$ at a distance $r$ from its centre $C$. When released, it reaches $C$ under the gravitational attraction of the ring. Its speed at $C$ will be

   1. A.$\sqrt{\frac{2Gm}{r}(\sqrt{2}-1)}$
   2. B.$\sqrt{\frac{Gm}{r}}$
   3. C.$\sqrt{\frac{2Gm}{r}\left(1-\frac{1}{\sqrt{2}}\right)}$
   4. D.$\sqrt{\frac{2Gm}{r}}$
   Show answer

   Answer: C