Q. The frequency of vibration of string is given by $v = \frac{P}{2l}\left\lbrack \frac{F}{m} \right\rbrack^{1/2}$. Here $p$ is number of segments in the string and $l$ is the length. The dimensional formula for $m$ will be
A) $\lbrack M^{0}LT^{- 1}\rbrack$
B) $\left\lbrack ML^{0}T^{- 1} \right\rbrack$
C) $\lbrack ML^{- 1}T^{0}\rbrack$
D) $\lbrack M^{0}L^{0}T^{0}\rbrack$
Explanation
$v = \frac{P}{2l}\left\lbrack \frac{F}{m} \right\rbrack^{1/2}$ $\Rightarrow v^{2} = \frac{P^{2}}{4l^{2}}\ \left\lbrack \frac{F}{m} \right\rbrack$ $\therefore m \propto \frac{F}{l^{2}v^{2}}$ $\Rightarrow \lbrack m\rbrack = \left\lbrack \frac{MLT^{- 2}}{L^{2}T^{- 2}} \right\rbrack = \lbrack ML^{- 1}T^{0}\rbrack$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.