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Question: A particle of mass m, initially at rest, is acted upon by a variable force F for a brief interval of...

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 = πF022m\frac{\pi F_{0}^{2}}{2m}

B

u = πT28m\frac{\pi T^{2}}{8m}

C

u = πF0T4m\frac{\pi F_{0}T}{4m}

D

u = F0T2m\frac{F_{0}T}{2m}

Answer

u = πF0T4m\frac{\pi F_{0}T}{4m}

Explanation

Solution

Change in momentum = area under F-t graph

mu = 12\frac { 1 } { 2 } {π.F0×T2}\left\{ \pi . \mathrm { F } _ { 0 } \times \frac { \mathrm { T } } { 2 } \right\} = πF0 T4\frac { \pi \mathrm { F } _ { 0 } \mathrm {~T} } { 4 }