Question bank/JEE Main/Physics

A bead can slide on a smooth straight wire and a particle of mass
m attached to the bead by a lightstring of length L. The particle is
held in contact with the wire and with the string taut and is then let
fall.
If the bead has mass 2 m then when the string makes an angle $\theta$
with the wire, the bead will haveslipped a distance

A$L(1 - cos\theta)$B$\ (L/2)\ (1 - cos\theta)$C$(L/3)(1 - cos\theta)$D$(L/6)(1 - cos\theta)$

Show answer and solution▾

Since the centre of mass will not move
2mx=my$\Rightarrow$y=2x
x + y = $L - L\cos\theta = L\left( 1 - \cos\theta \right)$
$3x = L(1 - cos\theta)$
⇒ $x = \frac{L(1 - cos\theta)}{3}$

Source: Grass-G / P-07 Physics paper 17 October.docx