A girl of mass 50 kg swinging on a cardle. If she moves with a velocity of `2 ms^(-1)` upwards in a direction making an angle `60^(@)` with the vertical, then the power generated is `(g= 9 . 8 ms^(-2))`

Options

A. 245 W
B. `490 sqrt(2) W`
C. `490 sqrt(3) W`
D. 980 W

Answer

C

Explanation

Given
Mass of the girl (m) = 50 g
Velocity (v) = 2 m/s
Angle `(theta) = 60^(@)`
`g = 9 . 8 m//s^(2)`
Work neede to displace to girl through a small arc of length dS is
` = mg sin 60^(@) xx ds`
Now work done in time dt
` = mg sin 60^(@) vdt`
Power at that instant ` = mg sin 60^(@) . v`
`= 50 xx 9 . 8 xx sin 60^(@) xx2`
`= 50 xx 9 . 8 xx (sqrt(3))/(2) xx2`
`= 25 xx 9.8 xx sqrt(3) xx2`
`= 490 sqrt(3) W`