Solved: PHYSICS Question for NEET

NEET PHYSICSMedium

A bullet from a gun is fired on a rectangular wooden block with velocity $u$ . When the bullet travels $24\text{ cm}$ through the block along its length horizontally, velocity of bullet becomes $u/3$ . 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:

30 cm

27 cm

24 cm

28 cm

Step-by-Step Solution

Identify the Principle: The resistive force assumed constant causes a constant deceleration ( $a$ ). We can use the Work-Energy Theorem or the kinematic equation $v^2 - u^2 = 2as$ [Class 11 Physics, Ch 5, Sec 5.6].
Analyze First Part of Motion:

Initial velocity $v_i = u$
Final velocity $v_f = u/3$
Displacement $s_1 = 24\text{ cm}$ $(u/3)^2 - u^2 = 2as_1$ $\frac{u^2}{9} - u^2 = 2a(24)$ $-\frac{8u^2}{9} = 48a \implies a = -\frac{u^2}{54}$

Analyze Total Motion: Let the total length of the block be $L$ . The bullet enters with $u$ and stops ( $v=0$ ) after traversing distance $L$ . $0^2 - u^2 = 2aL$ $-u^2 = 2\left(-\frac{u^2}{54}\right)L$ $1 = \frac{2L}{54} \implies L = 27\text{ cm}$
Alternative Method: Calculate the remaining distance $s_2$ from velocity $u/3$ to $0$ . $0^2 - (u/3)^2 = 2as_2$ $-\frac{u^2}{9} = 2\left(-\frac{u^2}{54}\right)s_2 \implies s_2 = 3\text{ cm}$ Total length $L = 24 + 3 = 27\text{ cm}$ .

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