The velocity v of a particle at time t is given by v = a t + t + c b , where a , b and c are constants. The dimensions of a , b and c are:NEET 2006

Using principle of homogeniety. Dimension of v = Dimension of a t = Dimenstion of t + c b ∴ a t = [ LT − 1 ] ⇒ ∣ a ∣ = [ T ] [ LT − 1 ] = [ LT − 2 ] And [ t ] [ b ] = [ LT − 1 ] [ b ] = [ LT − 1 ] [ T ] = [ L ] And c = T ⇒ c = [ T ]

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PhysicsUnit & DimensionMiscellaneousMedium2 minPYQ_2006

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The velocity $v$ of a particle at time $t$ is given by $v = a t + \frac{b}{t + c}$ , where $a, b$ and $c$ are constants. The dimensions of $a, b$ and $c$ are:NEET 2006

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Using principle of homogeniety. Dimension of $v =$ Dimension of $a t =$ Dimenstion of $\frac{b}{t + c}$ $∴ a t = [LT^{- 1}] \Rightarrow ∣ a ∣ = \frac{[ LT ^{- 1} ]}{[ T ]} = [LT^{- 2}] And \frac{[ b ]}{[ t ]} = [LT^{- 1}] [b] = [LT^{- 1}] [T] = [L] And c = T \Rightarrow c = [T]$

Stream:NEETSubject:PhysicsTopic:Unit & DimensionSubtopic:Miscellaneous

⏱ 2mℹ️ Source: PYQ_2006

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