NEET 2023 — Physics solution

NEET2023Physics

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:

A
$24$ cm
B
$28$ cm
C
$30$ cm
D
$27$ cm

Solution

Assume a constant retardation $a$ . Using $v^{2} = u^{2} - 2 a s$ :

After $24$ cm: $(\frac{u}{3})^{2} = u^{2} - 2 a (0.24) \Rightarrow 2 a (0.24) = \frac{8 u ^{2}}{9}$ .

For the bullet to stop after total distance $S$ : $0 = u^{2} - 2 a S \Rightarrow 2 a S = u^{2}$ .

Dividing: $\frac{0.24}{S} = \frac{8/9}{1} = \frac{8}{9} \Rightarrow S = 0.27$ m $= 27$ cm.

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