Answer:
2.4
Explanation:
We are given that
[tex]r_1=3.09 cm[/tex]
[tex]r_2=7.97 cm[/tex]
Let mass of each object =m
K.E of each object=E
We have to find the ration of sphere's angular speed to the spherical shell's angular speed.
Moment of inertia of sphere,[tex]I_1=\frac{2}{5}Mr^2_1[/tex]
Moment of inertia of spherical shell,[tex]I_2=\frac{2}{3}Mr^2_2[/tex]
Linear speed,[tex]v=\omega r[/tex]
K.E of sphere ,[tex]E_1=\frac{1}{2}mr^2_1\omega^2_1+\frac{1}{2}I_1\omega^2_1[/tex]
K.E of spherical shell,[tex]E_2=\frac{1}{2}mr^2_2\omega^2_2+\frac{1}{2}I_2\omega^2_2[/tex]
[tex]E_1=E_2=E[/tex]
[tex]\frac{1}{2}mr^2_1\omega^2_1+\frac{1}{2}I_1\omega^2_1=\frac{1}{2}mr^2_2\omega^2_2+\frac{1}{2}I_2\omega^2_2[/tex]
[tex]\omega^2_1(mr^2_1+I_1)=\omega^2_2(mr^2_2+I_2)[/tex]
[tex]\frac{\omega^2_1}{\omega^2_2}=\frac{mr^2_2+\frac{2}{5}mr^2_2}{mr^2_1+\frac{2}{3}mr^2_1}[/tex]
[tex]\frac{\omega_1}{\omega_2}=\sqrt{\frac{r^2_2\frac{7}{5}}{r^2_1\frac{5}{3}}}[/tex]
[tex]\frac{\omega_1}{\omega_2}=\frac{r_2}{r_1}\sqrt{\frac{21}{25}}=\frac{7.97}{3.09}\times \sqrt{\frac{21}{25}}=2.4[/tex]
