A rifle bullet loses 1/20th of its velocity in passing through a plank. least number of such planks

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5.Work, Energy, Power and Collision

hard

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

$5$

$10$

$11$

$20$

(c)Let the thickness of one plank is $s$ if bullet enters with velocity $u$ then it leaves with velocity

$v = \left( {u – \frac{u}{{20}}} \right) = \frac{{19}}{{20}}u$ from ${v^2} = {u^2} – 2as$

$⇒$ ${\left( {\frac{{19}}{{20}}u} \right)^2} = {u^2} – 2as$

$⇒$ $\frac{{400}}{{39}} = \frac{{{u^2}}}{{2as}}$

Now if the n planks are arranged just to stop the bullet then again from ${v^2} = {u^2} – 2as$ $0 = {u^2} – 2ans$

$⇒$ $n = \frac{{{u^2}}}{{2as}} = \frac{{400}}{{39}}$

$⇒$ $n = 10.25$ As the planks are more than $10$ so we can consider $n = 11$

Standard 11

Physics

easy

medium

(IIT-1980)

medium

(AIPMT-2004)

medium

hard