Answer
given,
length of slender rod =80 cm = 0.8 m
mass of rod = 0.39 Kg
mass of small sphere = 0.0200 kg
mass of another sphere weld = 0.0500 Kg
calculating the moment of inertia of the system
[tex]I = \dfrac{ML^2}{12}+\dfrac{m_1L^2}{4}+\dfrac{mL^2}{4}[/tex]
[tex]I = \dfrac{0.39\times 0.8^2}{12}+\dfrac{0.02\times 0.8^2}{4}+\dfrac{0.05\times 0.8^2}{4}[/tex]
[tex]I =0.032\ kg.m^2[/tex]
using conservation of energy
[tex]\dfrac{1}{2}I\omega^2 = (m_1-m_2)g\dfrac{L}{2}[/tex]
[tex]\omega=\sqrt{\dfrac{(m_1-m_2)gL}{I}}[/tex]
[tex]\omega=\sqrt{\dfrac{(0.05-0.02)\times 9.8 \times 0.8}{0.032}}[/tex]
[tex]\omega=2.71 \rad/s[/tex]
we know,
v = r ω
[tex]v = \dfrac{L}{2} \times 2.71[/tex]
[tex]v = \dfrac{0.8}{2} \times 2.71[/tex]
v = 1.084 m/s
