Question

A circular disc is rotating about its natural axis with angular velocity of $10{rads}^{-1}$. A second disc of same mass is joined to it coaxially. If the radius of the second disc is half of the first one, then they together rotate with an angular velocity of

• A. $2.5{rads}^{-1}$
• B. $5{rads}^{-1}$
• C. $8{rads}^{-1}$
• D. $6{rads}^{-1}$

Answer 1

The correct option is C $8{rads}^{-1}$

$r_2=r_2/2I_1=\frac{M{r_1}^2}{2}{I}_2=\frac{M{r_2}^2}{2}=\frac{M{r_1}^2}{8}Sincethereisnoexternaltorquesoconservationofangularmomentumisvalid{I}_1{\omega }_1=I_2{\omega }_2\Rightarrow \frac{M{r_1}^2}{2}\times 10=(\frac{M{r_1}^2}{8}+\frac{M{r_1}^2}{2})\times {\omega }_2{\omega }_2=8rad{s}^{-1}$