Question

A 60kg60 kg board that is 6 m6 m long is placed at the edge of a platform, with 4 m4 m of its length extending over the edge. The board is held in place by blocks of masses M1M1 and M2M2 placed with their centers of mass on either end. If M2=30kgM2=30kg , what is the minimum value of M1M1 needed to keep the board from falling off the platform? 30kg

Answer 1

Complete Question

The complete question is shown on the first and second uploaded image

Answer:

The minimum mass of $M_1 = 90\ kg$ correct option is  E

Explanation:

 Free body diagram of the set up  in the question is shown on the third uploaded image

  The mass of board is  $M = 60kg$

   The length of the board is $L = 6 \ m$

    The length extending over the edge is $L_e = 4 \ m$

    The second mass is  $M_2 = 30kg$

Now to obtain $M_1$ we take moment about the edge of the platform

               $M_1 g L_1 = Mg \frac{L}{2} + M_2 g L_2$

              $M_1 L_1 = M \frac{L}{2} + M_2 L_2$

  Substituting value  

               $M_1 (2) = (60)(1) + (30)(4)$

               $M_1 = 90 \ kg$