First slide

Work

Question

A rifle bullet loses 1/20^th of its velocity in passing through a plank. The least number of such planks required just to stop the bullet is

Moderate

A

5
B

10
C

11
D

20

Solution

Let the thickness of one plank is s
if bullet enters with velocity u then it leaves with velocity
$v = (u - \frac{u}{20}) = \frac{19}{20} u$
from $v^{2} = u^{2} - 2 as$
$\Rightarrow {(\frac{19}{20} u)}^{2} = u^{2} - 2 as \Rightarrow \frac{400}{39} = \frac{u^{2}}{2 as}$
Now if the n planks are arranged just to stop the bullet then again from $v^{2} = u^{2} - 2 as$
$0 = u^{2} - 2 ans$
$\Rightarrow n = \frac{u^{2}}{2 as} = \frac{400}{39}$
$\Rightarrow n = 10 .25$
As the planks are more than 10 so we can consider n = 11

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