Question

If the momentum of a ball is doubled, then the kinetic energy is A. 0.5 times larger. B. 2 times larger. C. 3 times larger. D. 4 times larger. E. 5 times larger.

Answer 1

Kinetic energy = p^2/2m

That is, kinetic energy of a body is directly proportional to the square of the momentum of that body.

So, if momentum doubles, its kinetic energy will increase 4 times.

option D is correct.

Answer 2

momentum = p = mv kinetic energy = k = 1/2 mv^2 k = 1/2 mv^2 times m/m (multiply by m & divide by m) k = 1/2 m^2v^2/m = > m^2v^2 = 2km p^2 = 2km p = squareroot 2km or p^2/2m = k now if we double momentum then kinetic will become 4 times option D