Q.A block of mass M on a horizontal smooth surface is pulled by a load of mass M/2 by means of a rope AB and string BC as shown in figure.The length and mass of the rope AB are L and M/2 respectively.As the block is pulled from AB=L to AB=0;its acceleration changes from
A) `(3g)/4` to `g`
B) `g/4` to `g/2`
C) `g/4` to `g`
D) `(3g)/2` to `2g`
The mass of the block on the smooth horizontal surface is M. A load of mass `M/2` that is suspended on the side pulls the block. The load is attached to the block by a vertical string and a horizontal rope of length L and mass `M/2` .
There is a force `(M/2)*g` with which the load is pulled downwards; this accelerates the block. Initially, the load pulls the block as well as the attached rope. the total mass of the two is `M/2 + M = (3M)/2` . The mass of the block, the rope and the load is 2*M. When a force `(M/2)*g` acts on this the resulting acceleration is `((M/2)*g)/((3M)/2+M/2)` = `g/4` .
When the block moves to the edge of the surface, the rope is hanging down. A force equal to `(M/2 + M/2)*g` pulls the load and the rope downwards. This results in an acceleration of the block equal to `(M*g)/(2*M) = g/2`
The correct option is B, acceleration changes from `g/4` to `g/2` .