Question

A particle of mass m is attached to a light rod of length l. Other end of the rod is hinged to wall. Minimum velocity (v0) that should be given to the particle in lowest position so that it completes a vertical circle

Answer 1

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Given that

• A particle of mass m is attached to a light rod of length l and other end of the rod is hinged to wall .

SOLUTION:-

• The particle should complete a vertical circles so that particles has to reach 2l height

so

Gain in Potential energy = Loss is kinetic energy

$&#10144 \: \: mgh \: = \frac{1}{2}m {v}^{2} \: \: \: \: \\ \\ &#10144 \: \: mg(2l) \: = \frac{1}{2}m {v}^{2} \\ \\ &#10144 \: \: v = \sqrt{4gl } \: \: \: \: \: \: \: \: \: \: \: \:$