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NEET PHYSICSEasy

The ratio of the dimension of Planck's constant and that of moment of inertia is the dimension of

A

Frequency

B

Velocity

C

Angular momentum

D

Time

Step-by-Step Solution

  1. Planck's Constant (hh): According to Planck's quantum theory, energy is given by E=hνE = h\nu . Thus, the dimensions of Planck's constant are [ML2T−2][T−1]=[ML2T−1]\frac{[ML^2T^{-2}]}{[T^{-1}]} = [ML^2T^{-1}] .
  2. Moment of Inertia (II): The formula for moment of inertia is I=∑mr2I = \sum mr^2 . Its dimensions are [M][L2]=[ML2][M][L^2] = [ML^2] .
  3. Ratio: Taking the ratio of their dimensions, we get [h][I]=[ML2T−1][ML2]=[T−1]\frac{[h]}{[I]} = \frac{[ML^2T^{-1}]}{[ML^2]} = [T^{-1}].
  4. Conclusion: The resulting dimension [T−1][T^{-1}] is the dimensional formula for frequency .
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