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2. motion in straight line — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysics2. motion in straight line1 Mark
MCQ
A car goes from $A$ to $B$ (without changing direction), during first part of journey its average speed is $V_1$ and for second part of journey average speed is $V_2$ . The ratio path length of second part to the path length of first part is $\sqrt {\frac{{{V_2}}}{{{V_1}}}} $ . In that case the average speed of total path is ....... of average speeds of both parts. Choose correct option of fill. 
  • A
    Airthmatic mean
  • ✓
    Geometric mean
  • C
    Harmonic mean
  • D
    Information is insufficient to answer
✓

Answer

Correct option: B.
Geometric mean
b
$\frac{S_{2}}{S_{1}}=\sqrt{\frac{V_{2}}{V_{1}}}, \quad V_{avg}=\frac{S_{1}+S_{2}}{t_{1}+t_{2}}=\frac{S_{1}+S_{2}}{\frac{S_{1}}{V_{1}}+\frac{S_{2}}{V_{2}}}$

$=\frac{1+\frac{S_{2}}{S_{1}}}{\frac{1}{V_{1}}+\frac{1}{V_{2}} \times \frac{S_{2}}{S_{1}}}=\frac{1+\sqrt{\frac{V_{2}}{V_{1}}}}{\frac{1}{V_{1}}+\frac{1}{V_{2}} \sqrt{\frac{V_{2}}{V_{1}}}}=\sqrt{V_{2} V_{1}}$

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