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Physics - Unit & Dimension Question with Solution | TestHub

PhysicsUnit & DimensionMiscellaneousEasy2 minPYQ_2020

PhysicsEasysingle choice

Planck's constant $(h)$ , speed of light in a vacuum $(c)$ and Newton's gravitational constant $(G)$ are three fundamental constants. Which of the following combinations of these has the dimension of length?

Options:

Answer:

Solution:

$L \propto h^{a} c^{b} G^{c}$

${[L]}^{1} = {[M^{1} L^{2} T^{- 1}]}^{a} {[L T^{- 1}]}^{b} {[M^{- 1} L^{3} T^{- 2}]}^{c}$

Solving,

$a = \frac{1}{2}, c = \frac{1}{2}, b = - \frac{3}{2}$

$\Rightarrow L = \frac{\sqrt{h G}}{c^{\frac{3}{2}}}$

Stream:NTA_ABHYAS_NEETSubject:PhysicsTopic:Unit & DimensionSubtopic:Miscellaneous

⏱ 2mℹ️ Source: PYQ_2020

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