An L-shaped object, made of thin rods of uniform mass density, is suspended with a string as shown in figure. If \[\,AB=BC\], and the angle made by AB with downward vertical is \[\theta \], then: [JEE Main 09-Jan-2019 Morning] |
A) \[\tan \,\theta \,\,=\,\,\frac{1}{3}\]
B) \[\tan \,\theta \,\,=\,\,\frac{1}{2}\]
C) \[\tan \,\theta \,\,=\,\,\frac{2}{\sqrt{3}}\]
D) \[\tan \,\theta \,\,=\,\,\frac{1}{2\sqrt{3}}\]
Correct Answer: A
Solution :
[a] |
\[mg\text{ }\frac{a}{2}\,{{d}_{1}}=\,\,mg{{d}_{2}}\] |
\[mg\frac{a}{2}\,\sin \,\theta \,\,\,=\,\,\,mg\,(\frac{a}{2}\,\cos \,\theta \,\,-\,\,a\sin \,\theta )\] |
\[\frac{\sin \,\theta }{2}\,\,=\,\,\frac{\cos \,\theta }{2}\,\,-\,\sin \,\theta \] |
\[\frac{3}{2}\,\sin \,\theta \,\,=\,\,\frac{\cos \,\theta }{2}\] |
\[\tan \,\theta \,\,=\,\,\frac{1}{3}\] |
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