Two balls of the

Yes. Both the balls will start rolling due to inertia of motion and they roll in the direction in which the train is moving. Due to the application of the brakes, the train comes to rest but due to inertia the ball tries to remain in motion, therefore, they continue to roll. The two balls will not roll with the same speed since, the masses of the ball are not same, therefore, the inertial force are also not same on both the balls thus the ball will move with difference speed.