A) \[\frac{{{v}_{2}}-{{v}_{1}}}{k-1}\]
B) \[\frac{k{{v}_{1}}-{{v}_{2}}}{k-1}\]
C) \[\frac{k{{v}_{2}}-{{v}_{1}}}{k-1}\]
D) \[\frac{{{v}_{2}}-{{v}_{1}}}{k}\]
Correct Answer: B
Solution :
| [b] When frequency is \[{{v}_{1}}\], | |
| \[h{{v}_{1}}=h{{v}_{0}}+\frac{1}{2}mu_{1}^{2}\] | ...(i) |
| When frequency is \[{{v}_{2}}\], | |
| \[h{{v}_{2}}=h{{v}_{0}}+\frac{1}{2}mu_{2}^{2}\] | ...(ii) |
| \[\because \] \[\frac{1}{2}mu_{1}^{2}-\frac{1}{k}\left( \frac{1}{2}mu_{2}^{2} \right)\] | |
| \[\therefore \] from Eq. (i) | |
| \[h{{v}_{1}}=h{{v}_{0}}+\frac{1}{2k}mu_{2}^{2}\] | ...(iii) |
| or \[\frac{1}{2}mu_{2}^{2}=kh{{v}_{1}}-kh{{v}_{0}}\] | ...(iv) |
| From Eqs. (ii) and (iv) |
| \[h{{v}_{2}}=h{{v}_{0}}+kh{{v}_{1}}-kh{{v}_{0}}\] |
| or \[{{v}_{0}}(1-k)=v{{ }_{2}}-k{{v}_{1}}\] |
| or \[{{v}_{0}}=\frac{k{{v}_{1}}-{{v}_{2}}}{k-1}\] |
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