Single Choice

The frequency of vibration of the string is given by $$v=\dfrac {p}{2l}\left [ \dfrac {F}{m} \right ]^{1/2}$$ 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$$[ML^{-1}T^{0}]$$
Correct Answer
D$$[M^0L^0T^{0}]$$

Solution

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

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