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Laws of Motion question

2023 · Q166
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Laws of Motion question

2023 · Q166

NEETPhysicsLaws of MotionMCQ+4 / −1

A bullet from a gun is fired on a rectangular wooden block with velocity uuu. When bullet travels 24 cm24 \mathrm{~cm}24 cm through the block along its length horizontally, velocity of bullet becomes u3\frac{u}{3}3u​. 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 :

  1. A
    24 cm24 \mathrm{~cm}24 cm
  2. B
    28 cm28 \mathrm{~cm}28 cm
  3. C
    30 cm30 \mathrm{~cm}30 cm
  4. D
    27 cm27 \mathrm{~cm}27 cm
View written solutionFree

Correct answer: D

$$B y v^{2}=u^{2}+2 a s$$

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

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

$$2 \mathrm{ax}=\frac{8 \mathrm{u}^{2}}{9}$$ ..... (1)

Similarly from starting

$v^{2}=u^{2}+2 a x$

$0=u^{2}-2 a x_{2}$

$$2 \mathrm{ax}_{2}=\mathrm{u}^{2}$$ ..... (2)

$\mathrm{By}~(1) /(2)$

$$\frac{x}{x_{2}}=\frac{8}{9}$$

$$\frac{24}{x_{2}}=\frac{8}{9}$$

$$\mathrm{x}_{2}=27 \mathrm{~cm}$$

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