In the arrangements shown, a block (of mass\[m\]) is being moved up against gravity, by two identical balloons, with constant speed\[v\]. The balloons carry \[+Q\]charge each and the connecting strings are massless. \[T\] and \[B\] respectively represent tension in each of the connecting strings and buoyant force on each of the balloons. Choose the incorrect alternative. |
A) \[B=\frac{mg}{2}\]
B) \[2T\cos \alpha =mg\]
C) \[T=\frac{{{Q}^{2}}}{16\pi {{\varepsilon }_{0}}{{l}^{2}}\sin \alpha }+\frac{mg}{2}\cos \alpha \]
D) \[2T\sin \alpha =\frac{{{Q}^{2}}}{16\pi {{\varepsilon }_{0}}{{l}^{2}}\sin \alpha }\]
Correct Answer: D
Solution :
Force between balloon, \[F=\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{{{Q}^{2}}}{{{\left( 2l\sin \alpha \right)}^{2}}}\] \[=\frac{{{Q}^{2}}}{16\pi {{\varepsilon }_{0}}{{l}^{2}}{{\sin }^{2}}\alpha }\] |
For the whole system, \[2B=mg,so\,B=\frac{mg}{2}\] Also 2T \[cos=mg.\] |
For horizontal direction, net force on the balloons is zero. |
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