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 mass `m` hits the cbe 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`.

Explanation

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