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 forrce 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)/( 4m)`
D. `(F_(0) T)/(2 m)`

Answer

C

Explanation

Area of `F-t` graph ` = (pi F_(0) T)/(4)`
(Area of ellipse `= pi ab)`
`Delta p = (pi F_(0) T)/(4)`
`m( u - 0) = (pi F_(0) T)/(4) rArr u = (pi F_(0) T)/(4m)`