Question

One particle has mass m and a second particle has mass 2m. The second particle is moving with speed v and the first with speed 2v. How do their kinetic energies compare?

a) Kinetic energy of the first particle is half that of the second
b) Kinetic energy of the first particle is equal to that of the second
c) Kinetic energy of the first particle is double that of the second
d) Kinetic energy is unrelated to mass and speed

Answer 1

The kinetic energy of the first particle with mass m and speed 2v is double that of the second particle with mass 2m and speed v. Therefore, the correct answer is (c) Kinetic energy of the first particle is double that of the second.

Step-by-step explanation:

The question is about comparing the kinetic energies of two particles, where one particle has mass m and the other has mass 2m. The first particle is moving with speed 2v, and the second particle is moving with speed v. The kinetic energy (KE) is given by the formula KE = 1/2 mv².

For the first particle with mass m and speed 2v, the kinetic energy is calculated as KE1 = 1/2 m(2v)² = 1/2 m×4v² = 2mv².

For the second particle with mass 2m and speed v, the kinetic energy is KE2 = 1/2 (2m)v² = mv².

Comparing KE1 and KE2, we can see that KE1 = 2mv² = 2 (mv²) = 2KE2. Thus, the kinetic energy of the first particle is double that of the second particle. Therefore, the correct option is (c) Kinetic energy of the first particle is double that of the second.