A bob of mass m is suspended by a light string of length L. It is imparted a horizontal velocity `v_(0)` at the lowest point A such that it completes a semicircular trajectory in the vertical plane with the string becoming slack only on reaching the topmost point, C this is shown in Fig. Obtain an expression for
the speeds at points B and C

Explanation

It is clear from Equation (3)
`v_(c) = sqrt(g L)`
AT B, the energy is
`E = (1)/(2) mv_(B)^(2) + ` mgL
Equating this to the energy at A and employing the result form (i), namely `v_(0)^(2)` = 5 gL
`(1)/(2) mv_(B)^(2) + mgL = (1)/(2) mv_(0)^(2)`
`= (5)/(2) mgl " ":. v_(B) = sqrt(3 gL)`