Question

A small ring of mass $m$ is connected with a particle of same mass by an ideal string & the whole system is released as shown in figure. Coefficient of friction between ring A and wire is $3/5$. Ring A will start sliding when connecting string will make an angle $(5\times x{)}^0$ with the vertical. Find $x$ (particle is free to move and ring can slide only)

Answer 1

$mglcos\theta =\frac{m{v}^2}{2}$
$T-mgcos\theta =2mgcos\theta$
$T=3mgcos\theta$
$3mgcos\theta sin\theta =\mu [mg+3mgco{s}^2\theta ]$
$\Rightarrow \theta ={45}^0$

Therefore, $x=9$