Question

The ratio of the dimensions of Plancks constant and that of the moment of inertia is the dimensions of

• A. frequency
• B. velocity
• C. angular momentum
• D. time

Answer 1

Answer: (A)

frequency

Answer 2

Energy, $E=h v$ $\Rightarrow h=$ Planck's constant $=\frac{E}{v}$ $\therefore [h] =\frac{[E]}{[v]}=\frac{\left[ ML ^{2} T ^{-2}\right]}{\left[ T ^{-1}\right]}$ $=\left[ ML ^{2} T ^{-1}\right]$ and $I=$ moment of inertia $=M R^{2}$ $\Rightarrow [I]=[ M ]\left[ I ^{2}\right]=\left[ MI ^{2}\right]$ Hence, $\frac{[h]}{[I]}=\frac{\left[ ML ^{2} T ^{-1}\right]}{\left[ ML ^{2}\right]}$ $=\left[ T ^{-1}\right]$ $=\frac{1}{[ T ]}=$ dimension of frequency