Question

The frequency of vibration of string is given by $ v=\frac{p}{2l}{{\left[ \frac{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}^{0}}L{{T}^{-1}}] $
• B. $ [M{{L}^{0}}{{T}^{-1}}] $
• C. $ [M{{L}^{-1}}{{T}^{0}}] $
• D. $ [{{M}^{0}}{{L}^{0}}{{T}^{0}}] $

Answer 1

Answer: (C)

$ v=\frac{p}{2l}{{\left[ \frac{F}{m} \right]}^{1/2}} $
Squaring the equation on either side, we have
$ {{v}^{2}}=\frac{{{p}^{2}}}{4{{l}^{2}}}\left( \frac{F}{m} \right) $
$ m=\frac{{{P}^{2}}F}{4{{l}^{2}}{{v}^{2}}} $
$ [m]=\frac{[ML{{T}^{-2}}]}{[{{L}^{2}}]{{[{{T}^{-1}}]}^{2}}}=[M{{L}^{-1}}{{T}^{0}}] $