COMEDK · Physics · 2. Units and Dimensions
Find the value of '\(n\)' in the given equation \(P=\rho^n v^2\) where '\(P\)' is the pressure, '\(\rho\)' density and '\(v\)' velocity.
- A \(\mathrm{n}=\dfrac{1}{2}\)
- B \(\mathrm{n}=1\)
- C \(\mathrm{n}=2\)
- D \(\mathrm{n}=3\)
Answer & Solution
Correct Answer
(B) \(\mathrm{n}=1\)
Step-by-step Solution
Detailed explanation
The dimensional formula for pressure \(P\) is \([M L^{-1} T^{-2}]\). The dimensional formula for density \(\rho\) is \([M L^{-3}]\). The dimensional formula for velocity \(v\) is \([L T^{-1}]\). Substituting these into the equation \(P = \rho^n v^2\), we get:…
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