NEETPhysicsWork, Power and Energy
Match List-I with List-II regarding a ball striking the ground and rebounding. List-I contains the percentage of kinetic energy lost during the collision, and List-II contains the corresponding ratio of the rebound velocity to the impact velocity ( v_f / v_i ). List-I (Percentage of KE lost) List-II (Ratio v_f / v_i ) (A) 36 % (I) 0.5 (B) 51 % (II) 0 (C) 75 % (III) 0.8 (D) 100 % (IV) 0.7 Choose the correct answer fro
Options
- A(A)-(III), (B)-(IV), (C)-(I), (D)-(II)
- B(A)-(IV), (B)-(III), (C)-(I), (D)-(II)
- C(A)-(III), (B)-(I), (C)-(IV), (D)-(II)
- D(A)-(I), (B)-(II), (C)-(III), (D)-(IV)
Correct answer
A. (A)-(III), (B)-(IV), (C)-(I), (D)-(II)
Step-by-step solution
Let initial kinetic energy be K_i and final kinetic energy be K_f . Since K = 1 2 mv^2 , the velocity ratio is v_f v_i = K_f K_i . If 36 % of kinetic energy is lost, 64 % is retained. K_f K_i = 0.64 v_f v_i = 0.64 = 0.8 . (A) matches (III). If 51 % of kinetic energy is lost, 49 % is retained. K_f K_i = 0.49 v_f v_i = 0.49 = 0.7 . (B) matches (IV). If 75 % of kinetic energy is lost, 25 % is retained. K_f K_i = 0.25 v_f v_i = 0.25 = 0.5 . (C) matches (I). If 100 % of kinetic energy is lost, 0 % is retained. K_f K_i =