A bullet from a gun is fired on a rectangular wooden block with v… - Vidyadip

MCQ

A bullet from a gun is fired on a rectangular wooden block with velocity $u$.When bullet travels $24\,cm$ through the block along its length horizontally, velocity of bullet becomes $\frac{u}{3}$. Then it further penetrates into the block in the same direction before coming to rest exactly at the other end of the block. The total length of the block is $........\,cm$

A
$30$
✓
$27$
C
$24$
D
$28$

✓

Answer

Correct option: B.

$27$

b
By $v^2=u^2+2 a s$

$\left(\frac{u}{3}\right)^2=u^2-2 a x$

$2 a x=u^2-\frac{u^2}{9}$

$2 a x=\frac{8 u^2}{9}.........(1)$

Similarly from starting

$v^2=u^2+2 ax$

$0= u ^2-2 ax _2$

$2 ax _2= u ^2..........(2)$

$By (1) /(2)$

$\frac{ x }{ x _2}=\frac{8}{9}$

$\frac{24}{ x _2}=\frac{8}{9}$

$x _2=27\,cm$

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