Question Detail
Question
The frequency of vibration of a string is given by f = (P/2l)√(F/m). Here P is number of segments in the string, F is the tension, and l is the length. The dimensional formula for m will be?
Correct Answer
Option A is the correct answer.
Detailed Explanation
f has dimensions [T⁻¹]. P is dimensionless. So [T⁻¹] = (1/[L]) × √([F]/[m]) = [L⁻¹] × √([MLT⁻²]/[m]). So √([MLT⁻²]/[m]) must have dimensions [T⁻¹L] → [MLT⁻²]/[m] = [T⁻²L²] → [m] = [MLT⁻²] / [T⁻²L²] = [ML⁻¹]. That's [ML⁻¹], not in options. Option A is [M⁰LT⁻¹] which is velocity. Maybe m is mass per unit length? Then [m] = [ML⁻¹]. Option A is [M⁰LT⁻¹], wrong. Possibly they want dimensions of m as mass per unit length.
Hint
Use dimensional analysis on the formula.