Q. A body of mass $M$ is hung by a long thread and a bullet of mass $m$ hits it horizontally with a velocity $v$ and gets embedded in the body. Then for the body and the bullet system
A) Momentum$= \left( \frac{Mm}{M + m} \right)v$
B) Kinetic energy$= \frac{1}{2}mv^{2}$
C) Momentum$= \ \frac{(M + m)mv}{M}$
D) Kinetic energy$= \frac{m^{2}v^{2}}{2(M + m)}$
Explanation
(d) Velocity of system $= \frac{mv}{m + M}$
KE of system $= \frac{1}{2}(M + m)\left( \frac{mv}{M + m} \right)^{2}$
$= \frac{m^{2}v^{2}}{2(M + m)}$
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Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.