First slide

Second law

Question

A gun applies a force F on a bullet which is given by $F = (100 - 0.5 \times 10^{5} t) N$ . The bullet emerges out
with speed 400 m/s. Then, find out the impulse exerted till force on bullet becomes zero. [AIIMS 2019]

Moderate

A

0.2 N-s
B

0.3 N-s
C

0.1 N-s
D

0.4 N-s

Solution

Force applied by gun, $F = (100 - 0.5 \times 10^{5} t) N$
Speed of bullet, v = 400 m/s
When F = 0, then 100 - 0.5 X 10⁵ t = 0
$\Rightarrow t = 2 \times 10^{- 3} s$
$Impulse, I = \int F d t = \int_{0}^{2 \times 10^{- 3}} (100 - 0.5 \times 10^{5} t) d t$
$= {[100 t - 0.5 \times 10^{5} \cdot \frac{t^{2}}{2}]}_{0}^{2 \times 10^{- 3}}$
$= 100 \times 2 \times 10^{- 3} - \frac{0.5 \times 10^{5}}{2} \times (4 \times 10^{- 6} - 0)$
$= 0.2 - 0.1 = 0.1 N - s$

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