A bag (mass M) hangs by a long thread and a bullet (mass m) comes horizontally with velocity v and gets caught in the bag. Then for the combined (bag + bullet) system [CPMT 1989; Kerala PMT 2002]

• A.             Momentum is \[\frac{mvM}{M+m}\]
• B.             Kinetic energy is \[\frac{m{{v}^{2}}}{2}\]
• C.             Momentum is \[\frac{mv(M+m)}{M}\]
• D.             Kinetic energy is \[\frac{{{m}^{2}}{{v}^{2}}}{2(M+m)}\]