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(B) Let the particle have speed $u$ at the horizontal position and speed $v$ at the highest point. For a light rod, the particle can complete the circ

Vedclass · Accepted Answer

$\sqrt{2gl}$

Vedclass · Answer

(B) Let the particle have speed $u$ at the horizontal position and speed $v$ at the highest point. For a light rod, the particle can complete the circle even if its speed at the highest point is zero $(v = 0)$.Applying the law of conservation of mechanical energy between the horizontal position and the highest point:Initial energy at horizontal position = Final energy at highest point$\frac{1}{2}mu^2 + mg(0) = \frac{1}{2}mv^2 + mgl$Since $v = 0$ for the minimum speed condition:$\frac{1}{2}mu^2 = mgl$$u^2 = 2gl$$u = \sqrt{2gl}$Thus, the minimum speed required at the horizontal position is $\sqrt{2gl}$.

$A$ particle is rotated in a vertical circle by connecting it to a light rod of length $l$ and keeping the other end of the rod fixed. The minimum speed of the particle when the light rod is horizontal for which the particle will complete the circle is

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