Question

An impulsive force $\left(F\right)$ acts on a body which changes with time $\left(t\right)$. The $F-t$ graph is shown below. The value of impulse in time $\pi \text{sec}$ will be:

• A. $350\text{N-s}$
• B. $200\text{N-s}$
• C. $250\text{N-s}$
• D. $300\text{N-s}$

Answer 1

The correct option is B $200\text{N-s}$

Given,
Impulsive force, $F=100\sin t$
Time, $t=\pi \text{sec}$
We know that
Impulsive force, $F=\frac{dp}{dt}$
$\Rightarrow$ Impulse $\Rightarrow dJ=dp=Fdt$
Integrating on both sides we get,
$J=\underset{p_1}{\overset{p_2}{\int }}dp=\underset{0}{\overset{\pi }{\int }}Fdt$
$\Rightarrow J=\underset{0}{\overset{\pi }{\int }}100\sin tdt$
$=100{[-\cos t]}_0^{\pi }$
$=-100\left[\right(-1)-1]$
$\Rightarrow J=200\text{N-s}$
The value of impulse in $\pi \text{sec}$ is $200\text{N-s}$
Hence, option (b) is the correct answer.