Find the mass of the hanging block which will prevent the smaller block from slipping over the triangular block. All the surfaces are frictionless and the strings and the pulleys are light. Given $m = M=1kg; cot\theta =2$

For $m$ not to slide over $M$, acceleration of the triangular block should be $g \tan \theta$ .

If $m_0$ is the required mass, then

                                $mg-T = m_0 \left(g\tan \theta \right)$            …(i)

and                                    $T =(M+m)g \tan \theta$

or                                      $T = 2g \tan \theta$                 …(ii)

                                    $cot \theta = 2$                            …(iii)

After simplifying above equation, we get $m_0=2 kg$ .