Physics - Unit & Dimension Question with Solution | TestHub

PhysicsUnit & DimensionMiscellaneousEasy2 minPYQ_2020

PhysicsEasysingle choice

If $C, R, L a n d I$ denote capacity, resistance, inductance and electric current respectively, the quantities having the same dimensions of time among the following are

(1) $C R$

(2) $\frac{L}{R}$

(3) $\sqrt{L C}$

(4) $L I^{2}$

Options:

Answer:

Solution:

$[C] = [M^{- 1} L^{- 2} T^{4} A^{2}], [R] = [M L^{2} T^{- 3} A^{- 2}]$

$[L] = [M L^{2} T^{- 2} A^{- 2}] a n d [I] = [M^{0} L^{0} T^{0} A]$

1. $[C R] = [M^{- 1} L^{- 2} T^{4} A^{2}] [{M L}^{2} T^{- 3} A^{- 2}]$

$= [M^{0} L^{0} T A^{0}]$

2. $\frac{[L]}{[R]} = \frac{[M L^{2} T^{- 2} A^{- 2}]}{[M L^{2} T^{- 3} A^{- 2}]} = [M^{0} L^{0} T A^{0}]$

3. $(\sqrt{LC}) = {([{ML}^{2} T^{- 2} A^{- 2}] \times M^{- 1} L^{- 2} A^{2})}^{1 / 2}$

$= [M^{0} L^{0} T A^{0}]$

4. $[L I^{2}] = [M L^{2} T^{- 2} A^{- 2}] {[M^{0} L^{0} T^{0} A^{1}]}^{2}$

$= [M L^{2} T^{- 2} A^{0}]$

Stream:NTA_ABHYASSubject:PhysicsTopic:Unit & DimensionSubtopic:Miscellaneous

⏱ 2mℹ️ Source: PYQ_2020

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