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 C $u=\frac{\pi F_{0}T}{4m}$

Let us assume that,

The initially particle was at rest. By the application of forces its momentum increases.

Final momentum of the particle $=$ area of $F-t$ graph

$mv=$ Area of semicircle

$=\frac{\pi r_1{r}_2}{2}$

$=\frac{\pi \left(F_0\right)\left(\frac{T}{2}\right)}{2}v$

$=\frac{\pi F_{0}T}{4m}$