The dimension of (a/b) in the equation p = (a-t2/bx), where p is pressure, x is distance and t is time is

Question

The dimension of (a/b) in the equation p = (a-t2/bx), where p is pressure, x is distance and t is time is (A) [LT-3] (B) [ML3T-1] (C) [M2LT-3] (D) [MT-2]

Tardigrade Admin · Accepted Answer

Given equation P=(a-t2/b x)=(a/b x)-(t2/b x) Applying the principal of homogeneity, we have [pressure] =[( text force / text area )]=[(a/b x)] or [ ML -1 T -2] =[(a/b)][(1/L)] or [(a/b)]=[ MT -2]

Q. The dimension of $\frac{a}{b}$ in the equation $p = \frac{a - t ^{2}}{b x}$ , where $p$ is pressure, $x$ is distance and $t$ is time is

$[L T^{- 3}]$

$[M L^{3} T^{- 1}]$

$[M^{2} L T^{- 3}]$

$[M T^{- 2}]$

Given equation $P = \frac{a - t ^{2}}{b x} = \frac{a}{b x} - \frac{t ^{2}}{b x}$
Applying the principal of homogeneity, we have
[pressure] $= [\frac{force}{area}] = [\frac{a}{b x}]$
or $[M L^{- 1} T^{- 2}] = [\frac{a}{b}] [\frac{1}{L}]$
or $[\frac{a}{b}] = [M T^{- 2}]$

Q. The dimension of ba​ in the equation p=bxa−t2​, where p is pressure, x is distance and t is time is

[LT−3]

[ML3T−1]

[M2LT−3]

[MT−2]