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NEET2016PhysicsUnits and DimensionsActual

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

  1. Ah G c 3 2
  2. Bh G c 5 2
  3. Ch c G
  4. Dc G ⁡ ⁡ h ⁡ 3 2

Correct answer

A. h G c 3 2

Step-by-step solution

L ∝ 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 = 1 2 , c = 1 2 , b = - 3 2 ⇒ L = h G c 3 2

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