Question

The magnitude of the force (in $N$) acting on a body varies with time $t$ (in $\mu s$) as shown. $AB,BC$ and $CD$ are straight line segments. The magnitude of the total impule of the force on the body from $t=4\mu s$ to $t=16\mu s$ is

• A. $5\times {10}^{-3}\text{Ns}$
• B. $5.8\times {10}^{-3}\text{Ns}$
• C. $5.8\times {10}^3\text{Ns}$
• D. $5\times {10}^3\text{Ns}$

Answer 1

The correct option is A $5\times {10}^{-3}\text{Ns}$

We know that,
$\text{Impulse}=\left(\text{Area of force-time graph under the specified interval}\right)$ in the interval of $(4\mu s$ to $16\mu s)$.
Hence the total area in the region of $(4\mu s$ to $16\mu s)$ is
$=\frac{1}{2}(800+200)\times 2\times {10}^{-6}+\frac{1}{2}\times 800\times 10\times {10}^{-6}$
$=5\times {10}^{-3}\text{Ns}$
The correct option is (a)