Dimensional formula of (a/b) satisfying P=(a - t2/bx) where P is pressure, x is distance and t is time will be

Question

Dimensional formula of (a/b) satisfying P=(a - t2/bx) where P is pressure, x is distance and t is time will be (A) ML1T- 1 (B) M2LT- 1 (C) ML0T- 2 (D) M0L- 1

Tardigrade Admin · Accepted Answer

P=(a - t2/b x)=(a/b x)-(t2/b x) By the principle of homogeneity. [.P].=( text force / text area )=(a/b [. x ].) textM textL- 1 textT- 2=(a/b)[(1/L)]⇒ (a/b)= textM textT- 2

Q. Dimensional formula of $\frac{a}{b}$ satisfying $P = \frac{a - t ^{2}}{b x}$ where $P$ is pressure, $x$ is distance and $t$ is time will be

$M L^{1} T^{- 1}$

$M^{2} L T^{- 1}$

$M L^{0} T^{- 2}$

$M^{0} L^{- 1}$

$P = \frac{a - t ^{2}}{b x} = \frac{a}{b x} - \frac{t ^{2}}{b x}$
By the principle of homogeneity.
$[P] = \frac{force}{area} = \frac{a}{b [ x ]}$
$M L^{- 1} T^{- 2} = \frac{a}{b} [\frac{1}{L}] \Rightarrow \frac{a}{b} = M T^{- 2}$

Q. Dimensional formula of ba​ satisfying P=bxa−t2​ where P is pressure, x is distance and t is time will be

ML1T−1

M2LT−1

ML0T−2

M0L−1