KCET · Physics · Semiconductors
The ratio of the dimensions of Planck constant and that of moment of inertia has the
dimensions of
- A time
- B frequency
- C angular momentum
- D velocity
Answer & Solution
Correct Answer
(B) frequency
Step-by-step Solution
Detailed explanation
Dimensions of Planck's constant \(=M L^{2} T^{-1}\)
Dimensions of moment of inertia \(=M L^{2}\)
Ratio of dimensions of Planck's constant and moment of inertia is \(\frac{[h]}{[I]}=\frac{M L^{2} T^{-1}}{M L^{2}}=T^{-1}\)
Dimension of frequency \(=T^{-1}\)
Dimension of velocity \(=L T^{-1}\)
Dimension of angular momentum \(=M L^{2} T^{-1}\)
Dimension of time \(=T\)
Thus, ratio of dimensions of Planck's constant and that of moment of inertia has the dimensions of frequency
Dimensions of moment of inertia \(=M L^{2}\)
Ratio of dimensions of Planck's constant and moment of inertia is \(\frac{[h]}{[I]}=\frac{M L^{2} T^{-1}}{M L^{2}}=T^{-1}\)
Dimension of frequency \(=T^{-1}\)
Dimension of velocity \(=L T^{-1}\)
Dimension of angular momentum \(=M L^{2} T^{-1}\)
Dimension of time \(=T\)
Thus, ratio of dimensions of Planck's constant and that of moment of inertia has the dimensions of frequency
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