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The time dependence of a physical quantity p is given by \( p = p_0 \exp(-αt^2) \), where α is a constant and t is the time. The constant α
- is dimensionless
- has dimensions T⁻²
- has dimensions T²
- has dimensions of p
Correct answer: has dimensions T⁻²
Solution
The argument of an exponential function must be dimensionless. Since the argument here is αt², the dimensions of α must cancel out the dimensions of t² (T²). Therefore, α has dimensions T⁻².
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