Work Energy And Power Question 276

Question: An iron ball of mass m, suspended by a light inextensible string of length from a fixed point, 0, is shifted by an angle $ {\theta_0} $ as shown so as to strike the vertical wall perpendicularly. The ’ maximum angle made by the string with vertical after the first collision, if e is the coefficient of restitution, is

Options:

A) $ {{\sin }^{-1}}{ 1-e^{2}( 1-\cos {\theta_0} ) } $

B) $ {{\cos }^{-1}}{ 1-e^{2}( 1-\cos {\theta_0} ) } $

C) $ {{\tan }^{-1}}{ 1-e^{2}( 1-\cos {\theta_0} ) } $

D) Zero

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Answer:

Correct Answer: B

Solution:

[b] Speed just before collision $ =\sqrt{2g\ell (1-\cos {\theta_0})} $

Speed just after collision $ =e\sqrt{2g\ell (1-\cos {\theta_0})} $

$ \frac{1}{2}me^{2}[2g\ell (1-\cos {\theta_0})]=mg\ell (1-\cos \theta ) $

From conservation of energy,

$ \therefore \theta ={{\cos }^{-1}}{ 1-e^{2}(1-\cos {\theta_0}) } $



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