Question

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

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

Answer 1

The correct option is D 120 ms${}^{-1}$

Let the velocity of the bullet after the collision be $v_b$ and the velocity of the wooden block after the collision be $v_w$.

Using conservation of energy for the wooden block,

$\frac{1}{2}m{v}_w^2=mgh$

$v_w=\sqrt{2gh}$

$v_w=\sqrt{2\times 9.8\times 0.1}=1.4m/s$

Applying conservation of momentum before and after the collision,

$0.01\times 400=m_w{v}_w+m_b{v}_b$

$4=2\times 1.4+0.01v_b$

$v_b=120m/s$