`A` bead is connected with a fixed disc of radius `R` by an inextensible massless string in a smooth horizontal plane. If the bead is pushed with a velocity `v_(0)` prependicular to the string, the bead moves in a curve and consequently collapses on the disc. Then

Options

A. Initial angular acceleration of the particle is `(v_(0)^(2))/(l^(2))`
B. Initial angular acceleration of the particle is `(v_(0)^(2)R)/(l^(3))`
C. Distance travelled by the particle till it collides with the disc is `(l^(2))/(2R)`
D. Distance travelled by the particle till it collides with the disc is `(l^(2))/(R )`

Answer

B, C

Explanation

`w=(v_(0))/(l-Rtheta)`
`(d theta)/(dt)=(v_(0))/((l-Rtheta))`
`underset(0)overset(l//R)(int)d theta(l-Rtheta)=underset(0)overset(t)(int)v_(0)dt`

`(l^(2))/(2R)=v_(0)t`
`t=(l^(2))/(2v_(0)R)`
Distance travelled `= v_(0)t=(l^(2))/(2R)......(i)`
`alpha=w(dw)/(d theta)=(v_(0))/(l-Rtheta)xx(v_(0)R)/(l-Rtheta)^(2)=(v_(0)^(2)R)/(l-Rtheta)^(3)`
for `theta=0`
`alpha =(v_(0)^(2)R)/(l^(3))`