Kinematics Question 547

Question: A body of mass $ m $ hangs at one end of a string of length l, the other end of Which is fixed. It’s given a horizontal velocity so that the string would just reach where it makes an angle of $ 60^{o} $ with the vertical. The tension in the string at mean position it’s [ it’sM Dhanbad 1994]

Options:

A) $ 2mg $

B)$ mg $

C) $ 3mg $

D) $ \sqrt{3}mg $

Show Answer

Answer:

Correct Answer: A

Solution:

When body is released from the position p (inclined at angle q from vertical) then velocity at mean position $ v=\sqrt{2gl(1-\cos \theta )} $ \ Tension at the lowest point = $ mg+\frac{mv^{2}}{l} $

$ =mg+\frac{m}{l}[2gl(1-\cos 60)] $

$ =mg+mg=2mg $



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