Two uniform ropes having linear mass densities m and 4m, length l. Each 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 figure (in the figure equilibrium position is shown). Now if the point A joint, is slightly displaced in downward direction and released. It is found that, the loop perform angular SHM with the period of the oscillation equal to 2N. The value of N (take l=150π2 metre) is _________.
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answer is 5.
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Detailed Solution
Let point A is displace in the downward direction by x.Net imbalance forces = mtotala[4mg(l+x)+mg(l−x)−{4m(l−x)g+m(l+x)g}]=(4m×2l+m×2l)aa=−3g5lx;ω=3g5l ⇒T=2π5l3g=10s
Two uniform ropes having linear mass densities m and 4m, length l. Each 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 figure (in the figure equilibrium position is shown). Now if the point A joint, is slightly displaced in downward direction and released. It is found that, the loop perform angular SHM with the period of the oscillation equal to 2N. The value of N (take l=150π2 metre) is _________.