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NTA Abhyas 2020

Exam: NTA Abhyas
Year: 2020
Subject: Physics
Chapter: Units and Dimensions

NTA Abhyas 2020 · Physics · Units and Dimensions

If v = (A)/(t) + Bt^ 2 + Ct^ 3 where v is velocity, t is time and...

If

v = \dfrac{A}{t} + Bt^{2} + Ct^{3}

where

v

is velocity,

t

is time and

A, B

and

C

are constants, then the dimensional formula of

B

is

Options

A $[ M^{0}LT^{0} ]$
B $[ ML^{0}T^{0} ]$
C $[ M^{0}L^{0}T^{} ]$
D $[ M^{0}LT^{- 3} ]$

Correct answer

D. $[ M^{0}LT^{- 3} ]$

Step-by-step solution

Dimension of velocity =

[ M^{0}L^{1}T^{- 1} ]

[ v ] = [ Bt^{2} ]

∴ [ B ] = \dfrac{[ v ]}{[ t^{2} ]} = \dfrac{[ M^{0} L^{1} T^{- 1} ]}{[ T^{2} ]} = [ L^{1} T^{- 3} ]

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