Question

A disc of mass $100g$ is kept floating horizontally in the air by firing bullets each of mass $5g$ with the same velocity at the same rate of $10$ bullets per second. The bullets rebound at the same speed in opposite direction. Then, the velocity of each bullet at the time of impact is: (Take $g=10m/s^2)$

• A. $1000m/s$
• B. $100m/s$
• C. $50m/s$
• D. $10m/s$

Answer 1

The correct option is D $10m/s$

Mass of the disc $m_d=100g=0.1kg$
Mass of the bullet $m_b=5g=0.005kg$

Let the speed of each bullet be $v$. The bullets rebound at the same speed in the opposite direction.
Hence change in speed of each bullet $=v-(-v)=2v$
Change in momentum of bullets per sec = Force applied on the disc
i.e $n\times m_b\times 2v=m_d\times g$
$10\times 0.005\times 2\times v=0.1\times 10$
$\Rightarrow v=\frac{1}{2\times 0.005\times 10}=10m/s$