1) Show that Change in K.E. in Perfectly Inelastic Collision has a negative magnitude.

In perfectly inelastic collions, there is permanent deformation in the colliding bodies, which do not recover.

Initial KE = Energy lost in deformation + Final KE.

Change in KE = Final KE - Initial KE = - Energy lost in deformation.

Since the energy lost is always positive, the above statement completely the required proof.

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