A rod PQ of mass M and length L is hinged at end P. The rod is kept horizontal by a mass less than string tied at a point Q as shown in figure. When string is cut, the initial acceleration rod is:

Explanation

To get the vertical speed given to the object to reach the top of the circle, law of conservation of energy can be used at a points (1) and (2)
Total energy at 1 = Total energy at 2
Potential energy at point 1 = 0
`"Kinetic energy at point" 1=1/2mv_(1)^(2)`
`"Potential energy at point" 2 = mg xx 2r`
`"Kinetic energy at point" 2 =1/2mv_(2)^(2)`
from eqn (1)
`0+1/2mv_(1)^(2)=2mgr+1/2mv_(2)^(2)`
`1/2v_(1)^(2)=2gr+1/2v_(2)^(2)`
`v_(1)^(2)-v_(2)^(2)=4gr`
In this case bob of mass m is connected with a rod of negligible mass, so the velocity of bob at highest point can be equal to zero i.e., `v_(2)=0`
`therefore "eqn". (2) "becomes"v_(1)^(2)=4gr, v_(1)=sqrt(4gr)ms^(-1) "or " v_(1)=2sqrt(gr)ms^(-1)`. The speed of bob obtained here is lesser than the speed obtained. It is only because of string is replaced by a massless rod here.