Directions : In the following question more than one of the answers given may be correct. Select the correct answer and mark it according to the code:
If a particle travels a linear distance at speed\[{{v}_{1}}\]and comes back along the same track at speed\[{{v}_{2}}.\] (1) Its average speed is arithmetic mean\[({{v}_{1}}+{{v}_{2}})/2\] (2) Its average speed is harmonic mean\[2{{v}_{1}}{{v}_{2}}/({{v}_{1}}+{{v}_{2}})\] (3) Its average speed is geometric mean\[\sqrt{{{v}_{1}}{{v}_{2}}}\] (4) Its velocity is zeroA) 1, 2 and 3 are correct
B) 1 and 2 are correct
C) 2 and 4 are correct
D) 1 and 3 are correct
Correct Answer: C
Solution :
If a particle moves a distance\[l\]at speed\[{{v}_{1}}\]and comes back with speed\[{{v}_{2}}\]then its average speed \[{{v}_{av}}=\frac{\Delta s}{\Delta t}=\frac{l+l}{\frac{l}{{{v}_{1}}}+\frac{l}{{{v}_{2}}}}=\frac{2{{v}_{1}}{{v}_{2}}}{{{v}_{1}}+{{v}_{2}}}\] = harmonic mean Further \[{{\overrightarrow{v}}_{av}}=\frac{\Delta \overrightarrow{r}}{\Delta t}=\frac{\overrightarrow{l}-\overrightarrow{l}}{\frac{l}{{{v}_{1}}}+\frac{l}{{{v}_{2}}}}=0\]
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