Question

The dimensional formula for Planck's constant and angular momentum are

• A. $\left[M{L}^2{T}^{-2}\right]and\left[ML{T}^{-1}\right]$
• B. $\left[M{L}^2{T}^{-1}\right]and\left[M{L}^2{T}^{-1}\right]$
• C. $\left[M{L}^3{T}^1\right]and\left[M{L}^2{T}^{-2}\right]$
• D. $\left[ML{T}^{-1}\right]and\left[ML{T}^{-2}\right]$

Answer 1

The correct option is B $\left[M{L}^2{T}^{-1}\right]and\left[M{L}^2{T}^{-1}\right]$

We know that $E=h\nu$
where dimensions of Energy, E are $M{L}^2{T}^{-2}$ and dimensions of frequency are inverse of Time Period, i.e. $T^{-1}$
Thus, $M{L}^2{T}^{-2}=\left[h\right]T^{-1}$
or, $\left[h\right]=M{L}^2{T}^{-1}$
Now, angular momentum, $L=I\omega$
where units of omega are inverse of time (rad/sec, where radian is dimensionless).
Units of I are $M{L}^2$ (because I is of the form $kM{x}^2$)
Thus $\left[L\right]=M{L}^2{T}^{-1}$