Question

A bullet is fired at a plank of wood with a speed of 100 $m/s$. After passing through the plank, its speed reduces to 49 $m/s$. An another bullet of same mass and same size but moving with a speed of 200 $m/s$ is fired at the same plank. The speed of this bullet after passing through the plank will be approximately (Assume the resistance offered by the plank is same for both the bullets.)

• A. 180 $m/s$
• B. 200 $m/s$
• C. 149 $m/s$
• D. 160 $m/s$

Answer 1

The correct option is A 180 $m/s$

Let $m$ be the mass of each bullet. Since the resistance offered by the plank is same for the two bullets, the amount of work done by the plank is the same for the two bullets. From work-energy principle, work done by the plank on the bullets will be equal to decrease in K.E. of the bullets.
Decrease in K.E. of 1st bullet
=$\frac{1}{2}m[{u^2}_1-{v^2}_1]$
Decrease in K.E. of 2nd bullet
=$\frac{1}{2}m[{u^2}_2-{v^2}_2]$
Since the work done is same in both cases, therefore decrease in K.E. will be same for both the cases.
$\frac{1}{2}m[{u^2}_1-{v^2}_1]=\frac{1}{2}m[{u^2}_2-{v^2}_2]\frac{1}{2}m[{100}^2-{49}^2]=\frac{1}{2}m[{200}^2-{v^2}_2]v_2=\sqrt{32401}{v}_2=180m/s$