Physics - Unit & Dimension Question with Solution | TestHub

PhysicsUnit & DimensionMiscellaneousEasy2 minPYQ_2020

PhysicsEasysingle choice

If gravitational constant $(G),$ planks constant $(h)$ and speed of light $(c)$ considered as fundamental physical quantities then find dimensional formula of time

Options:

Answer:

Solution:

Let

$[T] = {[G]}^{α} {[L]}^{β} {[C]}^{γ}$

$= {[M^{- 1} L^{3} T^{- 2}]}^{9} \cdot {[M L^{2} T^{- 1}]}^{β} {[L T^{- 1}]}^{γ}$

$\Rightarrow - α + β = 0$

$3 \propto + 2 β + γ = 0$

$- 2 α - β - γ = 1$

On solving we get

$α = \frac{1}{2}, β = \frac{1}{2}, γ = \frac{5}{2}$

Stream:NTA_ABHYASSubject:PhysicsTopic:Unit & DimensionSubtopic:Miscellaneous

⏱ 2mℹ️ Source: PYQ_2020

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