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

We know that, F Δ t = m Δ v i.e., impulse from 0 to 4 s = linear momentum gained in 4 s = area enclosed by graph from 0 to 4 s =(π r2/2) (r=2) =2 π N - s 1

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

$8 N - S$

$4 π N - s$

$2 π N - s$

$8 π N - S$

We know that,
$F Δ t = m Δ v$
i.e., impulse from 0 to $4 s =$ linear momentum gained in $4 s$
$=$ area enclosed by graph from 0 to $4 s$
$= \frac{π r ^{2}}{2} (r = 2)$
$= 2 π N - s^{1}$

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