Problems in Physics(Part—1)
Q1. Planck’s constant has dimensions ………, fill the blank Sol. Planck's constant (h) has dimensions of energy × time , which is equivalent to action . In terms of fundamental dimensions (Mass [M], Length [L], Time [T]), Planck’s constant has the dimensional formula: [h]=[M][L] 2 [T] −1 Explanation: Planck’s constant relates the energy (E) of a photon to its frequency (ν) via the equation: E=hν Energy (E) has dimensions [M][L] 2 [T] −2 (same as work or force × distance). Frequency (ν) has dimensions [T] −1 . Thus, solving for h: [h]=[E]/[ν]=[M][L] 2 [T] −2 /[T] −1 =[M][L] 2 [T] −1 Summary: The blank can be filled as: "Planck’s constant has dimensions [M][L] 2 [T] −1 ." Or, in words: "Planck’s constant has dimensions of energy multiplied by time (or action)." Q2. In the formula X = 3 YZ 2 X , and Z have dimensions of capacitance and magnetic induction, respectively. The dimensions of Y in MKSQ system are ………. ...