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 = $\frac{1}{2}$