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Question: The equation \(\frac{dv}{dt}\)= At – Bv is describing the rate of change of velocity of a body falli...

The equation dvdt\frac{dv}{dt}= At – Bv is describing the rate of change of velocity of a body falling from rest in a resisting medium. The dimensions of A and B are –

A

 LT -3, T\text{ LT}\text{ }^{\text{-3}}\text{, T}

B

 LT -3, T -1\text{ L}\text{T}^{\text{ -3}}\text{, T}\text{ }^{\text{-1}}

C

LT, T

D

LT, T -1\text{LT, T}\text{ }^{\text{-1}}

Answer

 LT -3, T -1\text{ L}\text{T}^{\text{ -3}}\text{, T}\text{ }^{\text{-1}}

Explanation

Solution

[A] = [dv/dt][t]=LT−3\frac{\lbrack dv/dt\rbrack}{\lbrack t\rbrack} = LT^{- 3}

[B] = [dv/dt][v]=T−1\frac{\lbrack dv/dt\rbrack}{\lbrack v\rbrack} = T^{- 1}