question_answer

A bullet of mass a and velocity b is fired into a large block of mass c. The final velocity of the system is           [AFMC 1981, 94, 2000; NCERT 1971; MNR 1998]

A)             \[\frac{c}{a+b}\cdot b\]

B)               \[\frac{a}{a+c}\cdot b\]

C)                         \[\frac{a+b}{c}.a\]          

D)                           \[\frac{a+c}{a}\cdot b\]

Correct Answer: B

Solution :

    Initially bullet moves with velocity b and after collision bullet get embedded in block and both move together with common velocity.             By the conservation of momentum             Þ a ´ b + 0 = (a + c) V Þ \[V=\frac{ab}{a+c}\]