Question

21. If P = Poe^ (alpha×t÷x+beta), where t is time and x is
displacement. Then dimension of alpha by beta is same as

(1) Velocity
(2) Acceleration
(3) (Displacement)?
(4) Time​

Answer 1

Answer:

The correct answer is option (1) Velocity

Explanation:

The given equation is,

$P = P_{0} e^{(\frac{\alpha t}{x} +\beta ) }$                ----------------- (i)

where t is time and x is displacement.

From the above equation, we can clearly figure out that $P$ and $P_{0}$ have the same dimensions.

So, as a result, according to dimensional analysis, the quantity $e^{(\frac{\alpha t}{x} + \beta ) }$  is dimensionless.

∴ Dimension of α/β = Dimensions of x/Dimensions of t

                                   = [L]/[T]

                                   = $[LT^{-1} ]$  = Dimension of velocity

Hence, the dimension of α/β is the same as the dimension of velocity.

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