question_answer

A vertical meter stick of mass 400 gm is pivoted at the top and is then displaced through an angle \[60{}^\circ \]. The increase in its potential energy is

A)  2 J                             

B) \[3\,J\]             

C)      \[0\,J\]             

D)      \[1\,J\]                                     

Correct Answer: D

Solution :

Center of mass of the stick lies at the midpoint and when the stick is displaced through an angle \[60{}^\circ \],it rises up to height h from the initial position. From the figure,\[h=\frac{l}{2}-\frac{l}{2}\cos \theta =\frac{l}{2}(1-\cos \theta )\] Hence, the increase in potential energy of the sick =\[=mgh=mg\frac{l}{2}(1-\cos \theta )=0.4\times 10\frac{1}{2}(1-\cos {{60}^{o}})=1\,J\] Hence, the correction option is (d).