Q131 / 180 · COMEDK 2013 · Physics

A bullet moving with a speed of $100 \mathrm{~ms}^{-1}$ can just penetrate two planks of equal thickness, then the number of such planks penetrated by the same bullet when the speed is doubled will be

  • A
    $6$
  • B
    $10$
  • C
    $4$
  • Correct answer
    D
    $8$

Solution

Given, $u_{1}=100 \mathrm{~ms}^{-1}$ $$ \Rightarrow u_{2}=2 \times u_{1}=2 \times 100=200 \mathrm{~ms}^{-1} $$ Using equation of motion, $$ v^{2}=u^{2}-2 a s \quad(\because \text { acceleration is negative }) $$ As, final velocity, $v=0$ $\Rightarrow \quad u^{2}=2 a s$ or $s=\frac{u^{2}}{2 a} \Rightarrow s \propto u^{2}$ $\therefore \quad \frac{s_{1}}{s_{2}}=\frac{u_{1}^{2}}{u_{2}^{2}}=\frac{(100)^{2}}{(200)^{2}}=\frac{1}{4}$ $\Rightarrow \quad s_{2}=4 s_{1}=4 \times 2$ planks $=8$ planks

Hence, the correct answer is option: 'D'.

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