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A Particle is attached to the lower end ...

A Particle is attached to the lower end of a uniform rod which is hinged at its other end as shown in the figure. The minimum speed given to the particle so that the rod performs circular motion in a verticle plane will be [length of the rod is l, consider masses of bopth rod and particle to be same]

Text Solution

Verified by Experts

The correct Answer is:
15
(At the higher point, angular velocity of the rod becomes zero)
Applying Mechanical energy conservation from A to B
`1/2(mI^(2))/3(omega^(2))+1/2(mI^(2))omega^(2) + mg(1/2)=(mg(3I)/2 + mg(21))/(omega^(2)[I^(2) + I^(2)/3]]=6gl`

`omega^(2) = (3 xx 6g)/(41) = (9g)/21`
`V_("min") = omegal = sqrt(9/2 gl) = sqrt(9/2 xx 10 xx 5) = 15 m//s`
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