Question

- In a relation, ma = PV - Qt2, where m, a, x and t are mass, acceleration, displacement and time 2 respectively, dimensional formula of is​

Answer 1

In a relation, ma = P$\sqrt{x}$+Qt², where m, a, x and t are mass, acceleration, displacement and time respectively.

We have to find the dimensional formula of $\frac{P}{Q^2}$

• dimension of m = [M]
• dimension of a = [LT¯²]
• dimension of x = [L]
• dimension of t = [T]

here, $ma=P\sqrt{x}+Qt^2$

from dimensional analysis,

dimensions of ma = dimensions of P√x = dimensions of Qt²

⇒dimension of m × dimension of a = dimension of P × dimension of √x = dimension of Q × dimension of t²

⇒ [M] × [LT¯²] = dimension of P × [L½] = dimension of Q × [T²]

∴ dimension of P = [MLT¯²]/[L½] = [ML½T¯²]

and dimension of Q = [MLT¯²]/[T²] = [MLT¯⁴]

now, dimensions of $\frac{P}{Q^2}$ = dimension of P/dimension of Q²

= $\frac{[ML^{1/2}T^{-2}]}{[MLT^{-4}]^2}$

= $[M^{-1}L^{-3/2}T^6]$

Therefore the dimensions of $\frac{P}{Q^2}=[M^{-1}L^{-3/2}T^6]$