# Show that minimum velocity required for a particle to loop a loop while going in verticle circle of radius r is underroot 5gr

1
by LilaKeer

2015-09-21T22:09:17+05:30

### This Is a Certified Answer

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
For a particle to revolve in a vertical loop, the minimum velocity that the particle has at the top of the circle must be just 0.  The tension in the string attached to the particle must be just above 0. .  The centripetal force of the particle  at the top of the circle must be just equal to the weight.
m g = m v2² / r         ,  v2 = velocity of particle at the top

KE of the particle at the bottom of the circle = initial KE = 1/2 m v²
v = initial velocity
applying the conservation of energy at the top of the circle:
1/2 m v² =  m g (2 r) + 1/2 m v2²
= 2 m g r + 1/2 m g r

simplyfying, we get :  v²  = 5 g r    and      v = √(5gr)

click on thanks button above please