(B) The argument of an exponential function must be dimensionless.Therefore,the dimensions of the exponent $[\alpha t^2]$ must be equal to the dimensi

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(B) The argument of an exponential function must be dimensionless.Therefore,the dimensions of the exponent $[\alpha t^2]$ must be equal to the dimensions of a dimensionless quantity,which is $1$.$[\alpha t^2] = [M^0 L^0 T^0] = 1$.Since $t$ represents time,its dimension is $[T]$.Thus,$[\alpha] [T^2] = 1$.$[\alpha] = \frac{1}{[T^2]} = [T^{-2}]$.Therefore,the constant $\alpha$ has the dimensions of $T^{-2}$.

Class 11 Physics Units, Dimensions and Measurement Dimensional Analysis, Uses and Limitations

Medium

The time dependence of a physical quantity $P$ is given by $P = P_0 e^{-\alpha t^2}$,where $\alpha$ is a constant and $t$ is the time. Then the constant $\alpha$ has:

A
Dimensionless
B
Dimensions of $T^{-2}$
C
Dimensions of $P$
D
Dimensions of $T^2$

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Units, Dimensions and Measurement

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Dimensional Analysis, Uses and Limitations

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The time dependence of a physical quantity $P$ is given by $P = P_0 e^{-\alpha t^2}$,where $\alpha$ is a constant and $t$ is the time. Then the constant $\alpha$ has:

Similar Questions

The equation of the stationary wave is $y = 2A \sin \left( \frac{2\pi ct}{\lambda} \right) \cos \left( \frac{2\pi x}{\lambda} \right)$. Which statement is not true?

Which of the following is a dimensional constant?

$L$, $C$, and $R$ represent the physical quantities inductance, capacitance, and resistance, respectively. The dimensional formula $ML^2T^{-4}A^{-2}$ corresponds to . . . . . . .

The time period of a body undergoing simple harmonic motion is given by $T=p^{a} D^{b} S^{c}$,where $p$ is the pressure,$D$ is density,and $S$ is surface tension. The values of $a, b,$ and $c$ respectively are

When a wave traverses a medium, the displacement of a particle located at $x$ at a time $t$ is given by $y = a \sin (bt - cx)$, where $a, b,$ and $c$ are constants of the wave. Which of the following is a quantity with dimensions?

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