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Can kinetic energy of a system be increa...

Can kinetic energy of a system be increased without applying any external force on the system?

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Yes
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Statement 1: Two spheres undergo a perfectly elastic collision. The kinetic energy of system of both spheres is always constant. [There is no external force on system of both spheres]. Statement 2: If net external force on a system is zero, the velocity of centre of mass remains constant.

Statement I: No external force acts on a system of two spheres which undergo a perfectly elastic head-on collision. The minimum kinetic energy of this system is zero if the net momentum of the system is zero. Statement II: If any two bodies undergo a perfectly elastic head-on collision, at the instant of maximum deformation. the complete kinetic energy of the system is converted to' deformation potential energy of the system.