Question:
The equation \( \left(p + \frac{a}{v^2}\right)(v - b) = \text{constant} \). The unit of \( a \) is
The equation \( \left(p + \frac{a}{v^2}\right)(v - b) = \text{constant} \). The unit of \( a \) is
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Equate dimensions of terms inside brackets to find unknown units.
Updated On: Apr 23, 2026
- Dyne × cm\(^5\)
- Dyne × cm\(^4\)
- Dyne/cm\(^3\)
- Dyne/cm\(^2\)
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The Correct Option is B
Solution and Explanation
Concept:
Terms inside bracket must have same units.
\[
p \sim \frac{a}{v^2}
\Rightarrow a \sim p \cdot v^2
\]
Step 1: Units.
\[ [p] = \text{Dyne/cm}^2,\quad [v] = \text{cm}^3 \] \[ [v^2] = \text{cm}^6 \]
Step 2: Compute.
\[ [a] = \frac{\text{Dyne}}{\text{cm}^2} \times \text{cm}^6 = \text{Dyne} \times \text{cm}^4 \] Conclusion: \[ {\text{Dyne} \times \text{cm}^4} \]
Step 1: Units.
\[ [p] = \text{Dyne/cm}^2,\quad [v] = \text{cm}^3 \] \[ [v^2] = \text{cm}^6 \]
Step 2: Compute.
\[ [a] = \frac{\text{Dyne}}{\text{cm}^2} \times \text{cm}^6 = \text{Dyne} \times \text{cm}^4 \] Conclusion: \[ {\text{Dyne} \times \text{cm}^4} \]
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