A pendulum string of length 
is moves up to a horizontal position (fig.) and released.
What should the minimum strength of the string be to withstand the tension as the pendulum passes through the position of equilibrium ? The mass of the pendulum is m .
Text Solution
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Sol. The pendulum passes through the equilibrium position moving along the arc of a circle of radius 
with a velocity v . At this moment the bob of the pendulum will possess a centripetal acceleration a = 
directed upwards. This acceleration is provided by the joint action of the force of gravity and the tension in the thread (fig.). By Newton's second law,
F – mg = m 
and hence F = m 
The velocity v is determined from the law of conservation of energy and is v = 
and therefore F = mg + 
= 3mg = 3P
where P is the weight of the bob. The thread must be able to support a load equal to three times the weight of the bob.
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