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The frequency upsilon of vibrations of ...

The frequency `upsilon` of vibrations of uniform string of length l and stretched with a force F is given by
`upsilon = (p)/(2l)sqrt((F)/(m))`
where p is the number of segments of the vibrating string and m is constant of the string. What is the dimensions of m?

A

`[ML^(-1)T^(-1)]`

B

`[ML^(-3)T^(0)]`

C

`[ML^(-2)T^(0)]`

D

`[ML^(-1)T^(0)]`

Text Solution

Verified by Experts

The correct Answer is:
D
Squaring both sides of the given relation, we get
`upsilon^(2)= (p^(2))/(4l^(2))(F)/(m)` or `m= (p^(2)F)/(4l^(2)upsilon^(2))`
`:.` dimensions of m
`("dimensions of m")/("dimensions of" l^(2) xx "dimensions of" upsilon^(2))` (`:.` p is a dimensionless quantity)
`=([MLT^(-2)])/([L^(2)][T^(-1)]^(2))= [ML^(-1)T^(0)]`
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