First slide

Dimensions of physical quantities

Question

Write the dimensions of a and b in the relation, $P = \frac{b - x^{2}}{a t}$ , where $P$ is power, $x$ is distance and $t$ is time.

Moderate

A

$[a] = = [M^{- 2} L^{0} T^{2}], [b] = [M^{1} L^{2} T^{0}]$
B

$[a] = = [M^{- 1} L^{0} T^{2}], [b] = [M^{2} L^{2} T^{0}]$
C

$[a] = = [M^{- 1} L^{0} T^{2}], [b] = [M^{1} L^{2} T^{0}]$
D

$[a] = = [M^{- 1} L^{0} T^{2}], [b] = [M^{0} L^{2} T^{0}]$

Solution

The given equation can be written as, $P a t = b - x^{2}$
Now,
$[P a t] = [b] = [x^{2}] o r [b] = [x^{2}] = [M^{0} L^{2} T^{0}] a n d [a] = \frac{[x^{2}]}{[P t]} = \frac{[L^{2}]}{[{ML}^{2} T^{- 3}] [T]} = [M^{- 1} L^{0} T^{2}]$

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