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1.Units, Dimensions and Measurement
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The frequency of vibration of string is given by $\nu = \frac{p}{{2l}}{\left[ {\frac{F}{m}} \right]^{1/2}}$. Here $p$ is 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
$[{M^0}{L^0}{T^0}]$
Solution
(c) $\nu = \frac{P}{{2l}}{\left[ {\frac{F}{m}} \right]^{1/2}}$
$ \Rightarrow {\nu ^2} = \frac{{{P^2}}}{{4{l^2}}}\left[ {\frac{F}{m}} \right]$
$\therefore m \propto \frac{F}{{{l^2}{\nu ^2}}}$
$ \Rightarrow [m] = \left[ {\frac{{ML{T^{ – 2}}}}{{{L^2}{T^{ – 2}}}}} \right] = [M{L^{ – 1}}{T^0}]$
Standard 11
Physics
