Question

The force-time $(F-t)$ graph for linear motion of a body initially at rest is shown in figure. The segments shown are circular, the linear momentum gained in $4\, s$ is

• A. $8\, N - s$
• B. $4 \pi N - s$
• C. $2 \pi N - s$
• D. $8 \pi N - s$

Answer 1

Answer: (C)

According to figure, radius of semi-circle, $r=2$
Linear momentum gained $=$ Impulse from $0$ to $4\, s$
$=$ Area enclosed by graph from $0$ to $4\, s$
$=\frac{\pi r^{2}}{2}=\frac{\pi(2)^{2}}{2}=2 \pi N - S$