Answer:1.26 m/s
Explanation:
Given
translation speed of ball =3.5 m/s
Moment of inertia of ball about com [tex]I=\frac{2}{5}mr^2[/tex]
Initial Energy
[tex]E_i=\frac{1}{2}mu^2+\frac{1}{2}I\omega _i^2(\omega =\frac{u}{r})[/tex]
Final Energy
[tex]E_f=\frac{1}{2}mv^2+\frac{1}{2}I\omega _f^2+mgh[/tex]
Equating energy as no energy loss take place
[tex]E_i=E_f[/tex]
[tex]\frac{1}{2}mu^2+\frac{1}{2}I\omega _i^2=\frac{1}{2}mv^2+\frac{1}{2}I\omega _f^2+mgh[/tex]
[tex]\frac{1}{2}mu^2+\frac{1}{2}\times \frac{2}{5}mr^2\times \left ( \frac{u}{r}\right )^2=\frac{1}{2}mv^2+\frac{1}{2}\times \frac{2}{5}mr^2\times \left ( \frac{v}{r}\right )^2+mgh[/tex]
m term get cancel
[tex]\left ( \frac{u^2}{2}\right )+\left ( \frac{2u^2}{10}\right )=\left ( \frac{v^2}{2}\right )+\left ( \frac{2v^2}{10}\right )+gh[/tex]
[tex]\frac{7}{10}u^2=\frac{7}{10}v^2+gh[/tex]
[tex]v^2=3.5^2-\frac{10}{7}\times 9.81\times 0.76[/tex]
[tex]v=\sqrt{1.6}=1.26 m/s[/tex]
