A) \[\left( \frac{{{\alpha }^{2}}+{{\beta }^{2}}}{\alpha \beta } \right)t\]
B) \[\left( \frac{{{\alpha }^{2}}-{{\beta }^{2}}}{\alpha \beta } \right)t\]
C) \[\frac{(\alpha +\beta )}{\alpha \beta }t\]
D) \[\frac{\alpha \beta t}{\alpha +\beta }\]
Correct Answer: D
Solution :
[d] From the figure we have, MP \[={{v}_{\max }}=\alpha \,{{t}_{1}}=\beta \,{{t}_{2}}\] But \[t={{t}_{1}}+{{t}_{2}}\] \[={{v}_{\max }}\left( \frac{1}{\alpha }+\frac{1}{\beta } \right)\] \[={{v}_{\max }}\left( \frac{\alpha +\beta }{\alpha \beta } \right)\] \[\therefore \,\,\,{{v}_{\max }}=\frac{\alpha \beta t}{\alpha +\beta }\] So, the correct answer is [d].You need to login to perform this action.
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