Two carts undergo an inelastic collision where they stick together. Cart A has an initial velocity v0, and the second cart B is initially at rest. After the collision, it is observed that the ratio of the final kinetic energy system to its initial kinetic energy is KfK0 = 1/6. Determine the ratio of the carts' masses, mBmA. (Assume the track is frictionless.)

Initial kinetic energy of the system = 1/2 mA v0²

If Vf be the final velocity of both the carts

applying conservation of momentum

final velocity

Vf = mAvo / (mA + mB)

kinetic energy (final) = 1/2 (mA + mB) mA²vo² / (mA + mB) ²

= mA²vo² / 2 (mA + mB)

Given 1/2 mA v0² / mA²vo² / 2 (mA + mB) = 6

mA v0² x (mA + mB) / mA²vo² = 6

(mA + mB) / mA = 6

mA + mB = 6 mA

5 mA = mB

mB / mA = 5.