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
Show Answer
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}) } $
