Answer:
(b)
\[{{v}_{1}}\,=\frac{1}{2\pi }\,\sqrt{\frac{{{s}_{1}}}{m}}\] and \[{{v}_{2}}\,=\,\frac{1}{2\pi
}\,\,\sqrt{\frac{{{s}_{2}}}{m}}\]
When
connected as shown, \[s={{s}_{1}}+{{s}_{2}}\]
\[\therefore
\] \[v=\,\frac{1}{2\pi
}\,\,\sqrt{\frac{{{s}_{1}}+\,{{s}_{2}}}{m}}\]
\[=\,\frac{1}{2\pi
}\,\sqrt{\frac{{{s}_{1}}}{m}+\,\frac{{{s}_{2}}}{m}}\,=\frac{1}{2\pi
}\,\sqrt{4{{\pi }^{2}}v_{1}^{2}\,+4{{\pi }^{2}}v_{2}^{2}}\]
\[=\sqrt{v_{1}^{2}+\,v_{2}^{2}}\]
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