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Consider a circular running track of radius "r". Two runners Anand and Ben are on the running track at a distance of "π r" from each other. They always run in a clockwise direction. The running track is such that the runners lose energy on one contiguous half of the track and gain energy in the other contiguous half of the track. Let both Anand and Ben have initial energy levels of "E".
[1] Let the runners consume or gain unit energy per unit distance traveled. Also. let the energy consumed or gained be independent of the distance traveled thus far when the energy levels are greater than zero. The runners come to a stop when all their energy is expended. Assuming that both runners run at the same constant speed "s". After traveling a distance of “2πnr” where n is a non-negative integer, what is the difference in energy levels of Anand and Ben?
(1) 0
(2) πr
(3) πnr
(4) π nrs[2] Assume that the position of Anand on the track is chosen randomly and Ben is at a distance of “πr” from Anand. What could have been the maximum possible difference in the energy levels between them during the process of completing one full circle?
(1) 0
(2) πr
(3) 2πr
(4)πr[3] Anand is at the start of the half circle that boosts energy and Ben at the start of the half circle that dissipates energy. Now, if the energy lost or gained per unit distance is proportional to the distance traveled thus far, with "k" being the energy lost or gained per unit distance travelled, what is the difference in the energy levels when Anand reaches the position of Ben and vice-versa?
1). 2kπr
2). kπ2 r2
3). kπ2 r2/2
4). kπr/2asked in JMET
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