  Question

# A long block A is at rest on a smooth horizontal surface. A small block B, whose mass is half of A, is placed on A at one end and projected along A with some velocity u. The coefficient of friction between the block is μ. The blocks will reach a final common velocity u3The work done against friction is two - thirds of the initial kinetic energy of B. Before the blocks reach a common velocity, the acceleration of A relative to B is 23μgBefore the blocks reach a common velocity the acceleration of A relative to B is 32μg

Solution

## The correct options are A The blocks will reach a final common velocity u3 B The work done against friction is two - thirds of the initial kinetic energy of B.  D Before the blocks reach a common velocity the acceleration of A relative to B is 32μgLet v be the final common velocity, Using conservation of momentum, mu=(m+2m)v, v=u3 Work done by friction is change in loss of kinetic energy, so 12mu2−12(3m)u29=12mu2[1−13]=23×12mu2. The work done agianst friction is two - thirds of the initial kinetic energy of B The force of friction between the blocks is μmg.  Acceleration of A(to the right) =a1=μmg2m=μg2 Acceleration of B (to the left)=a2=μmgm=μg Acceleration of A relative to B=a1−(−a2)=32μg.  Suggest corrections   