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.

Options

A. `u = (pi F_(0)^(2))/(2m)`
B. `u = (pi T^(2))/(8m)`
C. `u = (pi F_(0)T)/(4 m)`
D. `u = (F_(0)T)/(2m)`

Answer

C

Explanation

Impulse (I) = area under F ­ t graph
` = (pi r^(2))/(2) `
Now , Impulse (I) = Change in momentum
`rArr (pi r^(2))/(2) = (mu) rArr u = (pi rr )/(2m)`
`rArr u =(pi F_(0) (T//2))/(2m) = (pi F_(0)T)/(4 m)`