Question

A particle of mass m it’s accelerated to a velocity v. The momentum of the particle is p and the kinetic energy is k. A second particle of mass 1/2 m has the same momentum, p. This means that the kinetic energy it will be…

a) 1/4 k
b) 1/2 k
c) 2 k
d) 4 k

Answer 1

The kinetic energy of the second particle with half the mass of the first but the same momentum is double that of the first particle, making the correct option (c) 2k.

Step-by-step explanation:

If two particles have the same momentum p, their momenta are related by p = mv. Since particle 1 with mass m and particle 2 with mass 1/2 m have the same momentum, velocity v for the second particle must be greater to compensate for its smaller mass. We can calculate the kinetic energy for the second particle using the kinetic energy formula K.E. = ½ mv².

For particle 1, the kinetic energy k is given by k = ½ mv². For particle 2, let's call its velocity v2. We know that p = mv = ½ mv2, which implies v2 = 2v. The kinetic energy of particle 2 would then be K.E. = ½ (1/2 m) (2v)² = ½ (1/2 m) * 4v² = 2 (½ mv²) = 2k.

Therefore, the kinetic energy of the second particle is 2k, which means the correct answer is option (c).