Two uniform ropes having linear mass densities `m` and `4m` are joined to form a closed loop. The loop is hanging over a fixed frictionless small pulley with the lighter rope above as shown in the fig. (in the figure equilibrium position is shown). Now if point `A` (joint) is slightly displaced in downward direction and released, it is found that the loop performs SHM with the period of oscillation equal to `N`. Find the value of `N` (take `l=(150m)/(4pi^2)`,`g=10(m)/(s^2)`).

Explanation

Let point `B` is displace in the downwards direction by `x`. Net imbalance forces `=m_("total").a`
`[4mg(l+x)+mg(l-x)-{4m(l-x)g+m(l+m)g}]`
`=(4mxx2l+mxx2l)a`
`a=-((3g)/(5l))x`
`omega=sqrt((mg)/(5l))impliesT=2pisqrt((5l)/(3g))=5s`