Question

A bullet moving with speed $100\text{m/s}$ strikes a block and get embedded into it. If mass of the block is nine times that of the bullet, find the impulse imparted by the bullet to the block (in $\text{Ns}$), given mass of the bullet is $m\text{kg}$.

• A. $100\text{m}$
• B. $90\text{m}$
• C. $10\text{m}$
• D. $110\text{m}$

Answer 1

The correct option is B $90\text{m}$

Given mass of the bullet is $m\text{kg}$,
Therefore, mass of the block is $9m\text{kg}$
Initial velocity of bullet, $v_1=100\text{m/s}$
Let the common velocity of bullet + block $=v_2$

Applying momentum conservation,
$m_1{v}_1=m_2{v}_2$
$m\times 100=(m+9m)v_2$
$100m=10m{v}_2$
or $v_2=10\text{m/s}$

Therefore, impulse imparted by the bullet on the block, $J=9m\Delta v$
$J=9m(10-0)$
$J=90m\text{Ns}$