A) \[\sqrt{\frac{{{m}_{1}}}{{{m}_{2}}}}\]
B) \[\sqrt{\frac{{{m}_{1}}+{{m}_{2}}}{{{m}_{2}}}}\]
C) \[\sqrt{\frac{{{m}_{2}}}{{{m}_{1}}}}\]
D) \[\sqrt{\frac{{{m}_{1}}+{{m}_{2}}}{{{m}_{1}}}}\]
Correct Answer: B
Solution :
[b] \[{{T}_{1}}={{m}_{2}}g\] |
\[{{T}_{2}}=({{m}_{1}}+{{m}_{2}})g\] |
\[\text{Velocity}\,\,\propto \sqrt{T}\] |
\[\lambda \propto \sqrt{T}\] |
\[\frac{{{\lambda }_{1}}}{{{\lambda }_{2}}}=\frac{\sqrt{{{T}_{1}}}}{\sqrt{{{T}_{2}}}}\] |
\[\Rightarrow \] \[\frac{{{\lambda }_{2}}}{{{\lambda }_{1}}}=\sqrt{\frac{{{m}_{1}}+{{m}_{2}}}{{{m}_{2}}}}\] |
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