In the adjacent figure, a uniform cube of mass `m` and edge `l=2m` is lying at rest an a rough horizontal surface. A small ball of same mass m hits the cube at its top edge with horizontal speed `v_(0)` and sticks to it. Friction is so large that the cube can rotate about the edge `O` without sliding Calculate the minimum value of `v_(0)` (in `m//s`) so that the cube will topple. ignore any loss of energy due to friction at the edge `O` and take `sqrt(2)-1=0.4`

Answer

8

Explanation

Form COAM
`mv_(0)l=(8ml^(2))/3omega`
`impliesomega=(3v_(0))/(8l)`………….i
From COE, after collision
`1/2xx(8ml^(2))/3xxomega^(2)`
`=2mgxx(3l)/4xx(sqrt(2)-1)`………..ii
`=v_(0)=8m//s`