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. x = $\frac{1}{2}$, y = $\frac{1}{2}$
• B. x = -$\frac{1}{2}$, y = - $\frac{1}{2}$
• C. x = $\frac{1}{2}$, y = - $\frac{1}{2}$
• D. x = - $\frac{1}{2}$, y = $\frac{1}{2}$

Answer 1

The correct option is D x = - $\frac{1}{2}$, y = $\frac{1}{2}$

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 = $\frac{1}{2}$