Question

a particle in motion and connected to a string is just able to complete a vertical circle of radius R acceleration of the particle when its velocity becomes vertical is​

Answer 1

The minimum velocity to the lowest point of a particle is completely circle. So the tendency which becomes is maximum to the topmost circle.  

At the top, tension is given by T = mvT2/R - mg, where vT = speed of the particle at the top.  

=>   mvT2/R  = T + mg  

For vT to be minimum, T ≈ 0 => vT = √gR  

If vB be the critical velocity of the particle at the bottom, then from conservation of energy  

Mg(2R) +  1/2 mvT2  = 0 + 1/2 mvB2  

As vT = √gR => 2mgR + 1/2 mgR = 1/2 mvB2  

Answer 2

Answer:10root10 m/s^2