Question:

The frequency of vibration of string is given by $ v=\frac{P}{2l}{{\left[ \frac{F}{m} \right]}^{1/2}} $ Here $ p $ is number of segments in the string and $l$ is the length. The dimensional formula for $ m $ will be:

Updated On: Jun 20, 2022
  • $ \left[ {{M}^{0}}L{{T}^{-1}} \right] $
  • $ \left[ M{{L}^{0}}{{T}^{-1}} \right] $
  • $ \left[ M{{L}^{-1}}{{T}^{0}} \right] $
  • $ \left[ {{M}^{0}}{{L}^{0}}{{T}^{0}} \right] $
Hide Solution
collegedunia
Verified By Collegedunia

The Correct Option is C

Solution and Explanation

Put the dimensions for each physical quantity in the given relation. Given,
$v=\frac{p}{2 l}\left[\frac{F}{m}\right]^{1 / 2}$
Squaring the equation on either side, we have
$v^{2}=\frac{p^{2}}{4 l^{2}}\left[\frac{F}{m}\right] $
$\Rightarrow m=\frac{p^{2} F}{4 l^{2} v}$
Putting the dimensions of equations on RHS,
we get $F=\left[M L T^{-2}\right], l=[L], v=\left[T^{-1}\right],$
$p$ being a number is dimensionless, we have
${[m]=\frac{\left[M L T^{-2}\right]}{\left[L^{2}\right]\left[T^{-1}\right]^{2}}} $
$=\left[M L^{-1} T^{0}\right]$
Was this answer helpful?
0
0

Top Questions on Units and measurement

View More Questions

Concepts Used:

Physical World

The physical world includes the complications of the natural world around us. It is a type of analysis of the physical world around us to understand how it works. The fundamental forces that control nature are:

  • Gravitational Force is a universal force that exists as an outcome of mutual attraction between any two objects with respect to their masses.
  • Electromagnetic Force can be understood as the force that is present between the charged particles. The force is stated by Coulomb’s law.
  • Strong Nuclear Force is the force that ties the protons and neutrons in a nucleus. Of all the elemental forces in nature, a strong nuclear force is the strongest as its name suggests.
  • Weak Nuclear Force can only be noticed in some of the nuclear processes such as the beta decay of the nucleus.