Explanation:
It is given that,
Radius of baseball, r = 3.87 cm = 0.0387 m
Speed of baseball, v = 36.6 m/s
Angular speed, [tex]\omega=112\ rad/s[/tex]
Translational kinetic energy, [tex]E_T=\dfrac{1}{2}mv^2[/tex]...........(1)
Rotational kinetic energy, [tex]E_R=\dfrac{1}{2}I\omega^2[/tex]........(2)
I = moment of inertia
For a sphere, [tex]I=\dfrac{2}{5}MR^2[/tex]
Equation (2) becomes :
[tex]E_R=\dfrac{1}{5}Mr^2\omega^2[/tex]...........(3)
Dividing equation (1) and (3). We get :
[tex]\dfrac{E_T}{E_R}=\dfrac{5v^2}{2r^2\omega^2}[/tex]
[tex]\dfrac{E_T}{E_R}=\dfrac{5\times (36.6\ m/s)^2}{2(0.0387\ m)^2\times (112\ rad/s)^2}[/tex]
[tex]\dfrac{E_T}{E_R}=\dfrac{713}{4}=178.25[/tex]
Hence, this is the required solution.
