The frequency v of vibrations of uniform string of length l and stretched with a force F is given by v=(p/2 l) √(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 ?

Question

The frequency v of vibrations of uniform string of length l and stretched with a force F is given by v=(p/2 l) √(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]

Tardigrade Admin · Accepted Answer

Squaring both sides of the given relation, we get

v^{2} = \frac{p ^{2}}{4 l ^{2}} \frac{F}{m}

or

m = \frac{p ^{2} F}{4 l ^{2} v ^{2}}

∴

dimensions of

m

= \frac{dimensions of F}{dimensions of l ^{2} \times dimensions of v ^{2}}

(

∵ p

is a dimensionless quantity)

= \frac{[ M L T ^{- 2} ]}{[ L ^{2} ] [ T ^{- 1} ] ^{2}}

= [M L^{- 1} T^{0}]

Q. The frequency $v$ of vibrations of uniform string of length $l$ and stretched with a force $F$ is given by
$v = \frac{p}{2 l} \frac{F}{m}$
where $p$ is the number of segments of the vibrating string and $m$ is constant of the string. What is the dimensions of $m ?$

$[M L^{- 1} T^{- 1}]$

$[M L^{- 3} T^{0}]$

$[M L^{- 2} T^{0}]$

$[M L^{- 1} T^{0}]$

Q. The frequency v of vibrations of uniform string of length l and stretched with a force F is given by v=2lp​mF​​ where p is the number of segments of the vibrating string and m is constant of the string. What is the dimensions of m?

[ML−1T−1]

[ML−3T0]

[ML−2T0]

[ML−1T0]

Squaring both sides of the given relation, we get v2=4l2p2​mF​ or m=4l2v2p2F​ ∴ dimensions of m = dimensions of l2× dimensions of v2 dimensions of F​ (∵p is a dimensionless quantity) =[L2][T−1]2[MLT−2]​ =[ML−1T0]

Q. The frequency $v$ of vibrations of uniform string of length $l$ and stretched with a force $F$ is given by
$v = \frac{p}{2 l} \frac{F}{m}$
where $p$ is the number of segments of the vibrating string and $m$ is constant of the string. What is the dimensions of $m ?$

$[M L^{- 1} T^{- 1}]$

$[M L^{- 3} T^{0}]$

$[M L^{- 2} T^{0}]$

$[M L^{- 1} T^{0}]$