Plancks' constant has the dimensions of

Options

A. Energy
B. Momentum
C. Angular momentum
D. Power

Answer

C

Explanation

`E = hv`
`implies h` = planck.s constant = `E/V`
` implies [h] = ([E][ML^2 T^(-2)])/([V][T^(-1)]) = [ML^2 T^(-1)]`
(a) Linear momentum = mass `xx` velocity
or `p = m xx v`
`r [p] = [m] xx [v] = [m][LT^(-1)] = [MLT^(-1)]`
(b) Energy `[E] = [ML^2 T^(-2)]`
(c) Angular momentum = moment of inertia `xx ` angular velocity
or `L_m = I xx omega = m r^2 omega " " [ therefore I = mr^2]`
`implies [L_n] = [M][L^2][T^(-1)] = [ML^2 T^(-1)]`
(d) Power = force `xx ` velocity
or `P = F xx V`
`implies [P] = [MLT^(-2)][LT^(-1)] = [ML^2 T^(-3)]`