- 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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In a relation, ma = P+Qt², where m, a, x and t are mass, acceleration, displacement and time respectively.
We have to find the dimensional formula of
- dimension of m = [M]
- dimension of a = [LT¯²]
- dimension of x = [L]
- dimension of t = [T]
here,
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 = dimension of P/dimension of Q²
=
=
Therefore the dimensions of
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