Question

A $5 kg$ mass is rotating on a circular path of radius $1 m$ with angular velocity of $50 rad / sec$. If radius of path becomes $5 m$. The value of angular velocity will be

• A. $7 \,rad / s$
• B. $3\, rad / s$
• C. $4\, rad / s$
• D. $2 \,rad / s$

Answer 1

Answer: (D)

Angular momentum $L=m v r=m \omega r \times r=m \omega r^{2}$
$\therefore \frac{\omega_{2}}{\omega_{1}}=\left(\frac{r_{1}}{r_{2}}\right)^{2}$
$\Rightarrow \omega_{2}=\left(\frac{1}{5}\right)^{2} \times 50$
$=\frac{50}{25}=2 \,rad / s$