Question

A bullet of mass $20g$ has an initial speed of $1m/s$, just before it starts penetrating a mud wall of thickness $20cm$. If the wall offers a mean resistance of $2.5\times {10}^{-2}N$, the speed of the bullet after emerging from the other side of the wall is close to

• A. $0.4m/s$
• B. $0.3m/s$
• C. $0.7m/s$
• D. $0.1m/s$

Answer 1

The correct option is C $0.7m/s$

Given, mass of the bullet
$m=20g=20\times {10}^{-3}kg$
Initial speed of bullet $v_i=1m/s$
Thickness of mud wall
$x=20cm=20\times {10}^{-2}m$
$\text{Resistance offers by wall}=2.5\times {10}^{-2}N$
By work energy theorem
$W_{\text{resistance}}=\Delta K$
$F\cdot x=\frac{1}{2}m{v}_f^2-\frac{1}{2}m{v}_i^2$

$-2.5\times {10}^{-2}=\frac{1}{2}\times 20\times {10}^{-3}(v_f^2-1^2)$

$-0.5=v_f^2-1^2$

$v_f^2=0.5=\frac{1}{2}$

$v_f=\frac{1}{\sqrt{2}}m/s=0.7m/s$

Final Answer: (d)