Questions
Two discs of same moment of inertia rotating about their regular axis passing through centre and perpendicular to the plane of disc with angular velocities . They are brought into contact face to face coinciding the axis of rotation. The expression for loss of energy during this process is
detailed solution
Correct option is A
Initial angular momentum Iω1+Iω2 Let ω be angular speed of the combined system. Final angular momentum 2Iω∴ According to conservation of angular momentum Iω1+Iω2=2Iω or ω=ω1+ω22 initial rotational kinetic energy Ei=12Iω12+ω22Final rotational kinetic energy Ef=12(2I)ω2=12(2I)ω1+ω222=14Iω1+ω22∴ Loss of energy ΔE=Ei-Ef=I2ω12+ω22-I4ω12+ω22+2ω1ω2=I2ω12+ω22-ω12+ω22+2ω1ω22=I22ω12+2ω22-ω12-ω22-2ω1ω22=I4ω12+ω22-2ω1ω2=I4ω1-ω22Talk to our academic expert!
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A disc rotates freely with rotational kinetic energy E about a normal axis through centre. A ring having the same radius but double the mass of disc is now, gently placed on the disc. The new rotational kinetic energy of the system would be
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