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The frequency (n) of vibration of a stri...

The frequency `(n)` of vibration of a string is given as ` n = (1)/( 2 l) sqrt((T)/(m))` , where `T` is tension and `l` is the length of vibrating string , then the dimensional formula is

A

`[M^(0) L^(1) T^(1)]`

B

`[M^(0) L^(0) T^(0)]`

C

`[M^(1) L^(-1) T^(0)]`

D

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

Text Solution

Verified by Experts

The correct Answer is:
C
`n = (1)/( 2l) sqrt((T)/(m)) rArr n^(2) = (1)/( 4l^(2)) (T)/(m)`
` m = (T) / ( 4 l^(2) n^(2)) = [ (MLT^(-2))/( L^(2) xx T^(-2))] = [ML^(-1)]`
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Knowledge Check

  • The frequency of vibration of string is given by v = (p)/(2 l) [(F)/(m)]^(1//2) . Here p is number of segment is the string and l is the length. The dimension formula for m will be

    A
    `[M^(0) LT^(-1)]`
    B
    `[M L^(0) T^(-1)]`
    C
    `[ML^(-1) T^(0)]`
    D
    `[M^(0) L^(0) T^(0)]`

  • The frequency of vibration of string is given by v= p/(2l) [F/m]^(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
    `[ML^0 T^(-1)]`
    C
    `[ML^(-1) T^(0)]`
    D
    `[M^0 L^0 T^0]`

  • The frequency of vibration of string is given by v=p/(2l)[F/m]^(1//2) . Here p is number of segments in the string and l is the length. The dimensional formula for m will be

    A
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    B
    `[ML^(0)T^(-1)]`
    C
    `[ML^(-1)T^(0)]`
    D
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