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 vertical plane will be ___________ (in m/s)
[length of the rod is l=5m consider masses of both rod and particle to be same, `g=10m//s^(2)`]

Answer

15

Explanation

(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`