Question

A bead can slide on smooth straight wire and a particle of mass m is attached to the bead by a light string of length 'L'. The particle is held in contact with the string taut and is then let fall. if the bead has mass 2m. then when the string makes an angle with the wire the bead will have slipped a ditance​

Answer 1

The string bead will make an angle at L ( 1 - cos a)/3 .

Length of the light string = L (Given)

Mass of the bead = 2m (Given)

Let the distance moved be = x

Centre of the bead mass and particle must remain at the same X coordinate.

Thus,  

2m × 0 + m × l /3 = L/3

Moving at a distance -  

2mX + m (X+L (cosa)/3m

= 3X + Lcos a/3

On equating -  

(3X+L ( cos a) = L

X = L ( 1 - cos a)/3

Therefore, the string bead will make an angle at L ( 1 - cos a)/3 .