A body of mass $5gram$ is executing S.H.M. about a fixed point $O$. With an amplitude of $10cm$, its maximum velocity is $100cm/s$. Its velocity will be $50cm/s$ at a distance (in $cm$):

$\text{Step 1 - Calculating angular velocity}$

We know that, $V_{max}=A\omega$

         We have, $V_{max}=100cm/s$ and $A=10cm$

                       $\Rightarrow 100=10\omega$

                            $\Rightarrow \omega =10rad/s$

$\text{Step 2 - Calculating distance}$

We know that, $V=\omega \sqrt{A^2-y^2}$

We have $V=50cm/s$

$\Rightarrow 50=10\sqrt{10^2-y^2}$

$\Rightarrow 5=\sqrt{10^2-y^2}$

Squaring both sides

$\Rightarrow 25=100-y^2$

$\Rightarrow y^2=75$

$\Rightarrow y=5\sqrt{3}cm$