A) 2:1
B) 3:2
C) 3:4
D) 1:3
Correct Answer: D
Solution :
According to question\[2{{n}_{1}}=3{{n}_{2}}\] or \[\frac{2}{2{{\ell }_{1}}}\sqrt{\frac{T}{{{m}_{1}}}}=\frac{3}{2{{\ell }_{1}}}\sqrt{\frac{T}{{{m}_{2}}}}\] or \[\frac{{{\ell }_{1}}}{{{\ell }_{2}}}=\frac{2}{3}\sqrt{\frac{{{m}_{2}}}{{{m}_{1}}}}=\frac{2}{3}\sqrt{\frac{{{V}_{2}}\rho {{\ell }_{2}}}{{{V}_{1}}\rho {{\ell }_{1}}}}\] or \[\frac{{{\ell }_{1}}}{{{\ell }_{2}}}=\frac{2}{3}\sqrt{\frac{r_{1}^{2}}{r_{1}^{2}}}=\frac{2}{3}\sqrt{{{\left( \frac{1}{2} \right)}^{2}}}\]or \[\frac{{{\ell }_{1}}}{{{\ell }_{2}}}=\frac{1}{3}\] Hence, the correction option is [d].
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