A disc of mass m and radius R is moving on a smooth horizontal surface with the flat circular face on the surface. It is spinning about its centre with angular peed `omega` and has a velocity V (see figure). It just manages to hit a stick AB at its end A. The stick was lying free on the surface and stick to the disc. [The combined object becomes like a badminton racket]. Mass and length of the stick are m and 2R respectively. (a) Calculate the angular speed of the combined object assuming `V = R omega` (b) Calculate loss in kinetic energy. Why is energy lost ? (c) If `V = eta (R omega)`, loss in kinetic energy is minimum. Find `eta`. (Assume `omega` is given]

A disc of mass m and radius R is moving on a smooth horizontal surface

1.	A disc of mass m and radius R is moving on a smooth horizontal surface with the flat circular face on the surface. It is spinning about its centre with angular peed `omega` and has a velocity V (see figure). It just manages to hit a stick AB at its end A. The stick was lying free on the surface and stick to the disc. [The combined object becomes like a badminton racket]. Mass and length of the stick are m and 2R respectively. (a) Calculate the angular speed of the combined object assuming `V = R omega` (b) Calculate loss in kinetic energy. Why is energy lost ? (c) If `V = eta (R omega)`, loss in kinetic energy is minimum. Find `eta`. (Assume `omega` is given]
Answer» Correct Answer - (a) `omega_(0) =(9)/17omega` (b) `Delta E = (5)/(68)mV^(2) + (7)/(34)mR^(2)omega^(2) - (3)/(17)mV R omega` (c) `eta = (6)/(5)`

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