Question

The force $F$ acting on a particle of mass $m$ is indicated by the $\text{force - time}$ graph shown below. The change in momentum of the particle over the time interval from zero to $8\text{s}$ is

• A. $24\text{N s}$
• B. $12\text{N s}$
• C. $20\text{N s}$
• D. $6\text{N s}$

Answer 1

The correct option is B $12\text{N s}$

From Newton's second law of motion, we know that,

$F=\frac{\Delta p}{\Delta t}$

$\Rightarrow \Delta p=F\Delta t$

For an $F-t$ graph ,

$F\Delta t=$ Area under $F-t$ graph.

So, From the data given in the diagram,

$\Delta p=(\frac{1}{2}\times 2\times 6)-(3\times 2)+(3\times 4)$

[Area above $x-$axis is taken postive , while Area below $x-$ axis is taken negative]

$\Rightarrow \Delta p=+12\text{N-s}$.

Hence, option $\left(\text{c}\right)$ is the correct choice.