Question

The frequency of vibration ${}^{\prime }{f}^{\prime }$ of a mass ${}^{\prime }{m}^{\prime }$ 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 $x=-\frac{1}{2},y=\frac{1}{2}$

The frequency of oscillation spring mass system $=\frac{1}{2\pi }\sqrt{\frac{k}{m}}$

Where, $k$=spring constant

and $m$=mass with spring

And given frequency, $f=c{m}^x{k}^y$

Comparing above two frequency we get $x=-\frac{1}{2},y=\frac{1}{2}$