Question

A bullet is fired from a gun. The force on the bullet is given by $F=600-2\times 10^{5}t$ where $F$ is in newton and $t$ in second. The force on the bullet becomes zero as soon as it leaves the barrel. What is the average impulse imparted to the bullet?

• A. $\text{9 Ns}$
• B. $\text{1}\text{.8 Ns}$
• C. $\text{0} \text{.9 Ns}$
• D. $\text{0} \text{.3 Ns}$

Answer 1

Answer: (C)

Given, $ \, F=600-2\times 10^{5} \, t=0$
$\Longrightarrow \, \, t=3\times 10^{- 3} \, s$
Impulese $I=\displaystyle \int _{0}^{t} F \cdot d t$
$=\displaystyle \int _{0}^{3 \times \left(10\right)^{- 3}} \left(600 - 2 \times \left(10\right)^{5} \, t\right) d t$
$=\left[\right.600 \, t-10^{5} \, t^{2}\left]\right._{0}^{3 \times 10^{- 3}}=0.9 \, Ns$