Question

The force-time ($F-t$) curve of a particle executing linear motion is as shown in the figure. The momentum acquired by the particle in time interval from zero to $8$ second will be (in $Ns$):

• A. $-2$
  
• B. $4$
  
• C. $6$
  
• D. $0$
  

Answer 1

The correct option is D $0$

Area under the curve of force-time graph gives the change in momentum of the body during that time interval.

Area under the curve $=-\frac{\pi r^2}{4}+\frac{\pi r^2}{2}-\frac{\pi r^2}{4}$ where $r=2$

$⟹$ Area under the curve from $0$ to $8$ second $=0$

Thus change in momentum of the particle is also zero.