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

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 π N - s (C) 2 π N - s (D) 8 π N - s

Tardigrade Admin · Accepted Answer

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 =(π r2/2)=(π(2)2/2)=2 π N - S

Q. 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

$8 N - s$

$4 π N - s$

$2 π N - s$

$8 π N - s$

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 $4 s$
$= \frac{π r ^{2}}{2} = \frac{π ( 2 ) ^{2}}{2} = 2 π N - S$

Q. 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 4s is

8N−s

4πN−s

2πN−s

8πN−s