A bead under the inflence of gravity, sides down a frictionless wire whose `y` coordinate is changing with `x` co-ordinate as shown in the figure. Assume that at position `O`the wire is vertical and the bead passes this point with a given speed `v_(0)` downward. If the shape of the wire is such that the vertical component of velocity remains `v_(0)` at all time, find `(a+b+c)`, in the shape function of wire given by `y +((agv_(0)x)^(b/c))/(2g)` where `g` is gravitational acceleration.

Answer

8

Explanation

`v=sqrt(v_(0)^(2)+2gy)`
and `vsintheta=v_(0)` (as given in question)
`:.sintheta =(v_(0))/(sqrt(v_(0)^(2)+2gy))`
`:. tan theta=(v_(0))/(sqrt(2gy))`
`(dy)/(dx)=(v_(0))/(sqrt(2gh))`
`:. Y=((3gv_(0)x)^(2//3))/(2g)`
`:. a+b+c=8`