Question

A body of mass $5kg$ is acted on by a net force $F$ which varies with time $t$ as shown in graph. Then the net momentum in $SI$ units gained by the body at the end of $10$ seconds is

• A. $0$
• B. $100$
• C. $140$
• D. $200$

Answer 1

The correct option is C $140$

We know that the Newton's second law of motion is $F=\frac{\Delta p}{\Delta t}$ or change in momentum

or the $gain$ in momentum is $\Delta p=F\Delta t=\text{Area under the F-t graph}$

The net area till the end of $t=10s$ is consists of a trapezium with parallel side as $10second$ and $8-4=4second$

and the separation being $20N$ so area or momentum is $\frac{sum\times separation}{2}=\frac{(10+4)second\times 20N}{2}=140Newtonsecond$

Option c is correct.