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4-1.Newton's Laws of Motion
hard
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.
A
$u = \frac{{\pi F_0^2}}{{2m}}$
B
$u = \frac{{\pi {T^2}}}{{8m}}$
C
$u = \frac{{\pi {F_0}T}}{{4m}}$
D
$u = \frac{{{F_0}T}}{{2m}}$
Solution
(c) Initially particle was at rest. By the application of force its momentum increases. Final momentum of the particle $ = $ Area of $F – t$ graph
$⇒$ $mu = $ Area of semi circle
$mu = \frac{{\pi \;{r^2}}}{2}$
$ = \frac{{\pi \;{r_1}{r_2}}}{2}$
$ = \frac{{\pi \;({F_0})\;(T/2)}}{2}$
$⇒$ $u = \frac{{\pi \;{F_0}T}}{{4m}}$
Standard 11
Physics
