  Question

# Choose the correct statement(s) from the following:A body can have energy and yet no momentum.The general form of Newton’s second law of motion is .A body having momentum must necessarily have kinetic energy.The relative velocity of two bodies in a head-on collision remains unchanged in magnitude and direction.

Solution

## The correct option is C A body having momentum must necessarily have kinetic energy.The general form of Newton’s second law is Fext=dpdt=ddt(mv)=mdvdt+vdmdt The form Fext=ma is valid only if dmdt=0, i.e. if mass does not change with time. Hence choice (a) is incorrect.     Choice (b) is correct because a body at rest may have potential energy and yet no momentum. Choice (c) is also correct. A body has momentum if it has mass and velocity and a body having a mass and velocity must have kinetic energy. Choice (d) is incorrect because (as shown in Sec.9 in text) the relative velocity remains unchanged in magnitude and gets reserved in direction; (v2 – v1) = - (u2 – u1). Hence the correct choices are (b) and (c).  Suggest corrections   