Question

A bullet of mass $\text{'}a\text{'}$and velocity $\text{'}b\text{'}$ is fired into a large block of wood of mass $\text{'}c\text{'}$. The bullet gets embedded into the block of wood. The final velocity of the system is

• A. $\frac{b}{a+b}\times c$
• B. $\frac{a+b}{c}\times a$
• C. $\frac{a}{a+c}\times b$
• D. $\frac{a+c}{a}\times b$

Answer 1

The correct option is C

$\frac{a}{a+c}\times b$

Hint: Conservation of Momentum states that the initial and final momentum of the system remains the same if there is no external force on the system.

Step 1: Given data

Mass of bullet $m_1$ $=a$

Velocity of bullet $v_1$$=b$

Mass of block of wood $m_2$ $=c$

Step 2: Concept used

Conservation of Momentum

Step 3: Conservation of momentum defined

According to the conservation of momentum, the quantity called momentum that characterizes motion never changes in an isolated collection of objects; that is, the total momentum of a system remains constant.

$\Rightarrow m_1{v}_1+m_2{v}_2=\left(m_1+m_2\right)v$

Step 4: Finding the final velocity of the system

$$\begin{gathered} \Rightarrow m_1{v}_1+m_2{v}_2=\left(m_1+m_2\right)v \\ \Rightarrow a\times b+c\times 0=\left(a+c\right)v \\ \Rightarrow v=\frac{a}{a+c}b \end{gathered}$$

Hence, option C is correct.