Question

A bullet leaving the muzzle of a rifle barrel with a velocity $v$ penetrated a plank and loses one-fifth of its velocity. It then strikes second plank, which it just penetrates through. Supposing the average resistance to the penetration is same in both the cases, the ratio of the thickness of the planks will be:

• A. $\frac{9}{16}$
• B. $\frac{1}{4}$
• C. $\frac{1}{5}$
• D. $\frac{9}{25}$

Answer 1

The correct option is A $\frac{9}{16}$

For the first plate, if $F$ is the average force of resistance.
$k_i+v_i+w_F=k_f+u_f$
$\frac{1}{2}m{v}^2+0+F{d}_1=\frac{1}{2}m{\left(\frac{4v}{5}\right)}^2+0$ ($d_1$ = Thickness of the first plate)
$\Rightarrow F{d}_1=-\frac{9m{v}^2}{50}\dots \dots \left(1\right)$ ($v_f=\frac{4v}{5}$ since it loses $\frac{v}{5}$)
For the second plate,
$k_i+v_i+w_F=k_f+v_f$
$\frac{1}{2}m{\left(\frac{4v}{5}\right)}^2+0+F{d}_2=0+0$ ($d_2:$ Thickness of the second plate)
$F{d}_2=-\frac{8m{v}^2}{25}\dots \dots \left(2\right)$
$\left(1\right)÷\left(2\right)$
$\frac{d_1}{d_2}=\frac{9}{50}\times \frac{25}{8}=\frac{9}{16}$