A sack containing sand is tied to one end of a massless inextensible string, the other end of which is connected to a mass M.The string passes over a fixed pulley of mass 2M so that initially the system is balanced.The sack develops a small hole through which the sand leaks out at a constant rate B.Determine the velocity of the sack when one fourth of the sand is left .The mass of empty sack being M/5.Assume that the string does not slip over the pulley.

mass of sand is 9M/5 and we have to find the velocity of sack at time t=9M/5*1/4*1/B.

this problem can be solved by :

1.instantanious force balance at mass M.

2.torque equation at pulley's centre.

3.force balance of sack in terms of instantanious mass and time t.

take care that the equation for acceleration for the sack must be written in basic form and the differentiation of expression should involve instantanious mass change of sack.

the velocity of sand leaving the sack is the same as the velocity of sack and acc. zero!!!

momentum cant be conserved in virtical direction due to unbalanced force at sack.