A rifle bullets loses left(frac{1}{20}right)^{th} of its velocity in passing through a plank. Assumi

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5.Work, Energy, Power and Collision

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A rifle bullets loses $\left(\frac{1}{20}\right)^{th}$ of its velocity in passing through a plank. Assuming that the plank exerts a constant retarding force, the least number of such planks required just to stop the bullet is .............

A

$11$

B

$20$

C

$21$

D

Infinite

Solution

(a)

Let the retarding force by one block is $F$ and displacement inside one block is $x$.

So using work energy theorem for one block

$-F \cdot x=\frac{1}{2} m\left[\left(\frac{19}{20} v\right)^2-v^2\right] \ldots(1)$

Applying work energy theorem for $n$ blocks

$-F_{. n x}=\frac{1}{2} m\left[o-v^2\right]$

Using value of Fx from $\ldots (1$)

$\frac{1}{2} m\left[v^2-\left(\frac{19}{20} v\right)^2\right] n=\frac{1}{2} m\left[o-v^2\right]$

Solving for $n$

$n=10.25$

So, $11$ Planks

Standard 11

Physics

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