Question

A bullet of mass 10g moving horizontally with a velocity of 400 m/s strikes a wooden block of mass 2 kg which is suspended by a light inextensible string of length 5 m. As a result, the centre of gravity the block is found to rise a vertical distance 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. 120 m/s
• B. 160 m/s
• C. 100 m/s
• D. 80 m/s

Answer 1

The correct option is A 120 m/s

The correct option is A.

Mass of the bullet is $10g$

$Velocity=400m/s$

Mass of the wooden block is $2kg$

$Length=5m$

Let the velocity of the bullet and the block after the collision will be $v_1\&v_2$

The block rises $410cm=0.1m$

A/C Conservation of the energy of the block:

PE at the maximum height =KE at the bottom of the block,

$m_{2}gh=\frac{1}{2}{m}_2{v}_2^2$

$v_2=\sqrt{2gh}=\sqrt{2\times 9.8\times 0.1}=1.4m/s$

Let $u_1$ is the initial velocity of the bullet, then according to the conservation of momentum,

$m_1{u}_1=m_2{v}_2+m_1{v}_1$

$v_1=\frac{m_1{u}_1-m_2{v}_2}{m_1}$

$=\frac{0.01\times 400-2\times 1.4}{0.01}=120m/s$