Answer :
Answer:
6.48 m/s
Explanation:
We are given that
Mass,M=2 kg
Radius,R=0.25 m
Height,h=3 m
Moment of inertia of solid sphere=[tex]I=\frac{2}{5}MR^2[/tex]
We have to find the linear speed.
[tex]\omega=\frac{v}{R}[/tex]
By law of conservation of energy
[tex]mgh=\frac{1}{2}I\omega^2+\frac{1}{2}mv^2[/tex]
[tex]mgh=\frac{1}{2}I(\frac{v}{R})^2+\frac{1}{2}mv^2=\frac{1}{2}v^2(\frac{I}{R^2}+m)[/tex]
Where [tex]g=9.8m/s^2[/tex]
Substitute the values
[tex]2\times 9.8\times 3=\frac{1}{2}(\frac{2}{5R^2}MR^2+M)=\frac{7}{10}Mv^2=\frac{7}{10}(2)v^2[/tex]
[tex]v^2=\frac{2\times 9.8\times 3\times 10}{7\times 2}[/tex]
[tex]v=\sqrt{\frac{2\times 9.8\times 3\times 5}{7}}[/tex]
[tex]v=6.48m/s[/tex]