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(a) Can kinetic energy of a system be changed without changing its momentum? 

(b) Can momentum of a system be changed without changing its kinetic energy?

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(a) Yes;In explosion of a bomb or inelastic collision between two bodies as force is internal, momentum is conserved while kinetic energy changes.

(b) Yes; If a force acts perpendicular to motion, work done will be zero and so kinetic energy will remain constant. However, the force will change the direction of motion and so, the momentum, e.g., in case of uniform circular motion of a body KE is constant while momentum changes.

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