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If an unknown quantity, $ϕ = \frac{m a}{α} \log (1 + \frac{α l}{m a}) .$ where m = mass, a = acceleration and l = length.

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Correct option is C

Logarithm has no dimensions.∴ 1+αlma= dimensionless ∴ αlma=M0L0T0⇒ α=mal=MLT−2[L]=MT−2∵ Dimensions of ϕ= Dimensions of maα =MLT−2MT−2=[L]=M0LT0

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If an unknown quantity, ϕ=maαlog⁡1+αlma.where m = mass, a = acceleration and l = length.

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If an unknown quantity, $ϕ = \frac{m a}{α} \log (1 + \frac{α l}{m a}) .$ where m = mass, a = acceleration and l = length.