Two same masses are tied with equal length of strings and are suspended at the same point. One mass is suspended freely whereas another is kept in a way that string is horizontal as shown. This is given initial velocity u in vertical downward direction. It strikes the freely suspended mass elastically that is just able to complete the circular motion after the collision about point of suspension O. Magnitude of velocity u is :

Engineering

Physics

Conservation of Energy

Collision

Circular Motion in Vertical Plane

Question

Two same masses are tied with equal length of strings and are suspended at the same point. One mass is suspended freely whereas another is kept in a way that string is horizontal as shown. This is given initial velocity u in vertical downward direction. It strikes the freely suspended mass elastically that is just able to complete the circular motion after the collision about point of suspension O. Magnitude of velocity u is :

$\sqrt{3 gL}$

$\sqrt{2.5 gL}$

$\sqrt{2 gL}$

$\sqrt{gL}$

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$mgℓ = \frac{1}{2} m (v^{2} - u^{2})$

⟹ u² = v² –2gℓ = 3gℓ