Question

A particle of mass $m,$ initially at rest, is acted upon by a variable force $F$ for a brief interval of time $T.$ It begins to move with a velocity $u$ after the force stops acting. $F$ is shown in the graph as a function of time. The curve is a semicircle. Then-

• A. $u=\frac{\pi F_0^2}{2m}$
• B. $u=\frac{\pi T^2}{8m}$
• C. $u=\frac{\pi F_{0}T}{4m}$
• D. $u=\frac{F_{0}T}{2m}$

Answer 1

The correct option is A $u=\frac{\pi F_0^2}{2m}$

Numerically $F_0=\frac{T}{2}$

Since, $F_0$ and $\frac{T}{2}$ are radii.

Area $=\frac{\pi F_0^2}{2}=m(u-0)$

$\Rightarrow u=\frac{\pi F_0^2}{2m}.$