Answer:
[tex]v = \sqrt{16\cdot g \cdot L}[/tex]
Explanation:
The physical phenomenon is described by the Principles of Momentum Conservation and Energy Conservation:
Momentum
[tex]m \cdot v = M\cdot \frac{v}{2} + m \cdot v'[/tex]
Energy
[tex]\frac{1}{2}\cdot m \cdot v^{2} = \frac{1}{8}\cdot M \cdot v^{2} + \frac{1}{2}\cdot m \cdot v'^{2}[/tex]
[tex]\frac{1}{8}\cdot M\cdot v^{2} = 2\cdot M\cdot g \cdot L[/tex]
The minimum speed of the pendulum bob so that it could barely swing through a complete vertical cycle is:
[tex]\frac{1}{8}\cdot v^{2} = 2\cdot g\cdot L[/tex]
[tex]v^{2} = 16\cdot g\cdot L[/tex]
[tex]v = \sqrt{16\cdot g \cdot L}[/tex]
