Question

The frequency of vibration of a string is given by
\( \nu = \dfrac{p}{2l}\left(\dfrac{F}{m}\right)^{1/2} \)
Here, \( p \) is the number of segments in the string and \( l \) is the length. The dimensional formula for \( m \) will be:

• A. \([M^0LT^{-1}]\)
• B. \([ML^0T^{-1}]\)
• C. \([ML^{-1}T^0]\)
• D. [M⁰LT⁰]

Hint:

Always equate dimensions of both sides to find unknown quantities.

Answer 1

The Correct Option is C

Step 1: Dimension of frequency:
\( [\nu] = T^{-1} \) 

Step 2: Dimension of force:
\( [F] = MLT^{-2} \) |

Step 3: From the given equation:
\( T^{-1} = L^{-1}\left(\dfrac{F}{m}\right)^{1/2} \)
\( \Rightarrow T^{-2} = L^{-2} \cdot \dfrac{MLT^{-2}}{m} \)
\( \Rightarrow m = ML^{-1} \)