A solid ball of mass M and radius 'R' is rolling without slipping on a flat horizontal surface at an initial angular velocity ω 0 . It hits a small bump of height h . Assume that the ball

Question

A solid ball of mass M and radius 'R' is rolling without slipping on a flat horizontal surface at an initial angular velocity ω 0 ​ . It hits a small bump of height h . Assume that the ball pivots about the tip of the bump during and after impact. Which of the following statements are TRUE ?

TestHub · Accepted Answer

​ ∫ P x ​ d t = m v x ​ − m u x ​ ​ ⇒ ∫ P x ​ d t = − mω R cos θ − ( − m ω 0 ​ R ) … . ( 1 ) ​ ∫ P y ​ d t = m v y ​ − m u y ​ ​ ⇒ ∫ P y ​ d t = mω R sin θ ​ On solving eqn. (1), (2) and (3), we get ω = ω 0 ​ I + MR 2 ( I + MR 2 cos θ ) ​ ⇒ ω = ω 0 ​ ( 1 − 7 R 5 h ​ ) From conservation of energy ​ 2 1 ​ m v 2 + 2 1 ​ I ( ω ) m i n 2 ​ + 0 = 0 + m g h ​ ⇒ ω f ​ = R 1 ​ 7 10 ​ g h ​ ⇒ ω 0 ​ = 7 R − 5 h 7 ​ 7 10 g h ​ ​ ​

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