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Doubt & Answer Explanation

Doubt

sir,
A stone of mass 1kg is tied to a string of length 2.7mt and whirled in a vertical circle. If the ratio of maximum tension to minimum tension in the string is 4,then the speed at the top of the circular path is?

Answer Explanation

Write the free body diagram of the body at the lowest at the highest point.
Note that the tension is maximum at the lowest point and minimum at the highest point.



At point A,
Let the tension is T1 and velocity is v1.

Then,
T1 - mg = mv12/R  ............ (i)

At B, Both tension and the weight point downwards, towards the centre.

mg + T2 = mv22/R  .............(ii)

Apply conservation of energy between points A and B.

mv12/2 = mv22/2 + mg(2R) ......... (iii)


Also, it is being given in the question that
T1 / T2 = 4.  ............................... (iv)

That gives us four equations and four unknowns. Put the values of mass and radius and solve for v2.

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