COMEDK · Physics · 2. Units and Dimensions
The time dependence of a physical quantity P is give by \(\mathrm{P=P}_0 \exp \left(-\alpha t^2\right)\) where \(\alpha\) is a constant and \(t\) is time. The constant \(\alpha\) will
- A Have no dimensions
- B Have dimensions as that of \(\mathrm{P}\)
- C Have dimensions equal to that of \(\mathrm{Pt}^2\)
- D Have dimensions of \(t^{-2}\)
Answer & Solution
Correct Answer
(D) Have dimensions of \(t^{-2}\)
Step-by-step Solution
Detailed explanation
The given equation is \(P = P_0 \exp(-\alpha t^2)\). In any exponential function of the form \(e^x\), the exponent \(x\) must be dimensionless. Therefore, the term \(\alpha t^2\) must be dimensionless. \([\alpha t^2] = [M^0 L^0 T^0] = 1\). Since \(t\) represents time, its…
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