A bullet P of mass 30 g moving with a speed of 200 m/s penetrates a target and comes to rest after travelling a distance of 10 cm inside it. Another bullet Q of mass 20 g moving with a speed of 300 m/s penetrates

Question

Quantrex Academy · Accepted Answer

Correct answer: B. (4)/(3)

Using the work-energy theorem, the work done by the resistive force is equal to the change in kinetic energy of the bullet.

F \times s = \dfrac{1}{2} m u^2 \Rightarrow F = \dfrac{m u^2}{2 s}

For bullet

P

:

F_P = \dfrac{30 \times 10^{-3} \times (200)^2}{2 \times 0.10} = \dfrac{30 \times 10^{-3} \times 40000}{0.2} = 6000 \text{ N}

For bullet

Q

:

F_Q = \dfrac{20 \times 10^{-3} \times (300)^2}{2 \times 0.20} = \dfrac{20 \times 10^{-3} \times 90000}{0.4} = 4500 \text{ N}

The ratio of the average resistive forces is:

\dfrac{F_P}{F_Q} = \dfrac{6000}{4500} = \dfrac{4}{3}

Answer:

\dfrac{4}{3}

A bullet P of mass 30 g moving with a speed of 200 m/s penetrates a...

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