If two particles have equal momenta, are their kinetic energies equal?

a) yes, always

m1v1 = m2v2 by the question
for KE to equal m1v1^2 = m2v2^2 (I cancelled the 1/2)
But lets call m1v1 = m2v2 = X
so in KE Xv1 = Xv2
so KE are equal if v1 = v2

it’s D. momentum is a product of mass*velocity p = mv.
Object 1 has mass m1 = 10kg and velocity v1 = 10 m/s, so p1 = (10 kg)(10 m/s) = 100 kgm/s.
Object 2 has mass m2 = 5 kg and velocity v2 = 20 m/s, so p2 = (5 kg)(20 m/s) = 100 kgm/s.
Both objects have different masses and velocities, but the same momentum, p1 = p2.
Kinetic energy of Object 1 is KE = 1/2 m1 v1^2 = 1/2 (10 kg) (10 m/s)^2 = 500 J.
Kinetic energy of Object 2 is KE = 1/2 m2 v2^2 = 1/2 (5 kg) (20 m/s)^2 = 1000 J.
Both kinetic energies are different.
This is one example of a proof that proves answer choice D.

Both c and e are correct.
If they have same mass, then they have to have same speed as their momenta is same.
similarly, their mass is same if they have same speed and momenta.
Kinetic energy will same if they have have mass and speed. But only same momenta is not sufficient. Raymond gives a good example below.

• Author
• Recent Posts

Answer Prime

This is the collective voice of the talented editorial team at Answerprime.com. Committed to delivering high-quality content, this account represents the collaborative efforts of knowledgeable experts. With a passion for research and a dedication to accuracy, Answerprime brings you insightful articles across various subjects. Explore a diverse range of expertise and perspectives curated by the editorial team through the lens of Answerprime.

Latest posts by Answer Prime (see all)

• How many teaspoons of nyquil are you supposed to take? - March 12, 2025
• Why Can I not Access Loadouts In MWII Offline Multiplayer - March 12, 2025
• In herman melville’s moby-duck, what is queequeg’s job aboard the boat? - March 12, 2025