Question

The frequency of vibration f of a mass m suspended from a spring of spring constant K is given by a relation of this type $f=C{m}^x{K}^y$; where C is a dimensionless quantity. The value of x and y are:

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

By putting the dimensions of each quantity both sides, we get $\left[T^{-1}\right]=\left[M{]}^x\right[M{T}^{-2}{]}^y$
Now comparing the dimenstions of quantities in both sides, we get $x+y=0$ and $2y=1$
$\therefore x=-\frac{1}{2}$,
$y=\frac{1}{2}$.