 # A non zero ext. force acts on a systems of particles. The velocity and acceleration of the centre of mass are found to be v0 and a0 at an instant t. It is possible thata)v0=0, a0=0  b)v0= 0, a0 ≠0   (c) v0 ≠ 0, a0=0Answer given is b which is true but even (a) can be true e.g. if given net ext force provides torque...about the central axis then object would rotate leading to velocity and acc. of CM zero! So is a correct? 10 years ago

Even in the case  where the net external force provides torque, the system will not only rotate about central axis but its centre of mass will also get accelerated in direction of force according to the Newtons second law. So (a) cant be a valid statement.

However in the case where the central axis of the system is fixed , the system will only rotate but its CM will not accelerate in the direction of motion but this case is different. Here the force provided by thing used to keep the central axis fixed will have to provide a counter force to stop the acceleration of CM.