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Question: A bullet of mass a and velocity b is fired into a large block of mass c. The final velocity of the s...

A bullet of mass a and velocity b is fired into a large block of mass c. The final velocity of the system is

A

ca+b⋅b\frac{c}{a + b} \cdot b

B

aa+c⋅b\frac{a}{a + c} \cdot b

C

a+bc.a\frac{a + b}{c}.a

D

a+ca⋅b\frac{a + c}{a} \cdot b

Answer

aa+c⋅b\frac{a}{a + c} \cdot b

Explanation

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

⇒ a × b + 0 = (a + c) V ⇒ V=aba+cV = \frac { a b } { a + c }