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Defining Kinetic Energy

Two point mas...

Question

Two point masses M are connected to the light rod of length L and it is free to rotate in vertical plane as shown. Calculate the minimum horizontal velocity given to lower mass M so that it completes the circular motion is vertical plane.

A

$\sqrt{8 g L}$

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B

$\sqrt{10 g L}$

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C

$\sqrt{\frac{48 g L}{5}}$

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D

$\sqrt{\frac{54 g L}{5}}$

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Solution

The correct option is C
$\sqrt{\frac{48 g L}{5}}$

By energy conservation

$K_{i} + U_{i} = K_{f} + U_{f} \Rightarrow \frac{1}{2} m V^{2} + \frac{1}{2} m \frac{V^{2}}{4} = m g (2 l) + m g (4 l) \Rightarrow v = \sqrt{\frac{48 g l}{5}}$

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