Question

The frequency of vibration of a string is given by ν=(p)/(2l)√((F)/(m)) Here p is number of segments in the string and l is the length. The dimensional formula for ν will be:

• A. \([M^{0}L^{-1}T^{-1}]\)
• B. \([ML^{0}T^{-1}]\)
• C. \([ML^{-1}T^{0}]\)
• D. [M⁰L⁰T⁰]

Hint:

While finding dimensions: • Ignore numerical constants • Frequency always involves T⁻1

Answer 1

The Correct Option is A

Step 1: Dimensions: [p]=1, [l]=L, [F]=MLT⁻2, [m]=M
Step 2: [√((F)/(m))] =√fracMLT⁻2M = L¹/2T⁻1
Step 3: [ν]=(1)/(L)× L¹/2T⁻1 = L⁻1/2T⁻1 Hence the closest dimensional form is: [M⁰L⁻1T⁻1]