Question

A bullet of mass $10g$ moving horizontal with a velocity of $400m{s}^{-1}$ strikes a wood block of mass $2kg$ which is suspended by light inextensible string of length $5m$. As result, the centre of gravity of the block found to rise a vertical distance of $10cm$. The speed of the bullet after it emerges horizontally from the block will be:

• A. $100m{s}^{-1}$
• B. $80m{s}^{-1}$
• C. $120m{s}^{-1}$
• D. $160m{s}^{-1}$

Answer 1

The correct option is C $120m{s}^{-1}$

Let the velocity of the block after emerging the bullet is $v_1$ and the speed of the bullet is $v_2$.

Apply the momentum conservation,

$mv+0=m_1{v}_1+m{v}_2$

$\frac{10}{1000}\times 400=2v_1+\frac{10}{1000}\times v_2$

$4=2v_1+0.01\times v_2$ (1)

From the work energy theorem, we have,

$m_{1}gh=\frac{1}{2}{m}_1{v_1}^2$

$2\times 10\times 0.1=\frac{1}{2}\times 2\times {v_1}^2$

$v_1=1.414m/s$

Substituting the value of $v_1$ in equation (1), we get

$4=2\times 1.414+0.01\times v_2$

$v_2=117.15m/s$

Thus, the speed of bullet after it emerges is $117.15m/s$.