Physics, asked by keyanpatel9411, 2 months ago

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

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Answered by abhi178
3

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]

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