A ball is bouncing elastically with a speed 1 m/s between walls of a railway compartment of size 10 m in a direction perpendicular to walls. The train is moving at a constant velocity of 10 m/s parallel to the direction of motion of the ball. As seen from the ground, a) the direction of motion of the ball changes every 10 seconds b) speed of ball changes every 10 seconds c) average speed of ball over any 20 seconds intervals is fixed d) the acceleration of ball is the same as from the train
Correct options are B) , C) and D) The speed of the ball when travelling in the same direction as that of the train is (10+1)m/s=11m/s. The speed of the ball just after collision is 9m/s in the opposite direction. Thus, it changes after the collision. Time taken by the ball travelling from one end to other to collide =110=10s. Thus, option (b) is correct. For the first 10 seconds the speed of the ball is 11m/s. For the next 10 seconds the speed of the ball is 9m/s. The total distance covered by the ball is 20m. The total time taken by the ball to do that is 20 seconds. Thus, average speed during these 20 seconds =1m will be uniform for every 20 seconds. Thus, option (c) is correct. For the first 10 seconds the speed of the ball is 11m/s. For the next 10 seconds the speed of the ball is 9m/s. The total distance covered by the ball is 20m. The total time taken by the ball to do that is 20 seconds. Thus, average speed during these 20 seconds =1m will be uniform for every 20 seconds. Thus, option (c) is correct. The train is not accelerating itself and is moving with a constant speed. It thus acts as an inertial frame of reference. Earth/ground is also an inertial frame of reference. Thus, the acceleration will be same in both the frames. Option (d) is correct.
