Question

The magnitude of force acting on a body varies with time as shown in the figure. The magnitude of total impulse of the force on the body from $t= 0$ to $t=16μs$ is-

• A. $6\times 10^{- 3}Ns$
• B. $5.8\times 10^{- 3}Ns$
• C. $8.4\times 10^{- 3}Ns$
• D. $7.6\times 10^{- 3}Ns$

Answer 1

Answer: (B)

Impulse $=\displaystyle \int F d t$ = area under curve
Area $=\left(200 \times 4 + \frac{1}{2} \times 2 \times \left(200 + 800\right) + \frac{1}{2} \times 10 \times 800\right)\times 10^{- 6}$
Area $=\left(800 + 1000 + 4000\right)\times 10^{- 6}$
Area $=5800\times 10^{- 6}=5.8\times 10^{- 3}\text{Ns}$