A) 1 Joule
B) \[1.5\] Joule
C) 3 Joule
D) 6 Joule
Correct Answer: C
Solution :
The mass of the rod is distributed all over its length. In such a situation, the entire mass can be considered to be concentrated at its\[C.G\]. Now in the given problem to calculate the increase in potential energy, we must calculate the change in height of the\[C.G\]. If in general, the length of the rod is\[l\], then the initial position of the \[C.G.\] is \[\frac{l}{2}\] from the top end, as shown in the figure below: When the rod is displaced through \[\theta \] from the vertical, the vertical distance of the new position of \[C.G.\] from the top end is given by distance \[OC\] in the figure shown below: In triangle\[OCB\], \[\frac{OC}{OB}=\cos \theta \] or, base\[(OC)=\]hypotanuse\[(OB)\cos \theta \] \[=\frac{l}{2}\cos \theta \] Thus, the displacement in the\[C.G.=OA-OC\] \[=\frac{l}{2}-\frac{l}{2}\cos \theta =\frac{l}{2}(1-\cos \theta )\] Substituting\[l=1\,\,m\] and \[\theta ={{60}^{o}}\] we get displacement in\[C.G.\Delta h=\frac{1}{2}(1-\frac{1}{2})\] \[=\frac{1}{4}=0.25m\] Now, increase in\[PE=mg\Delta h\] \[=1.2\times 9.8\times 0.8=3\,\,J\]You need to login to perform this action.
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