InterviewSolution
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InterviewSolution
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Two metal discs, one with radius `r` and mass `m` and the other with radius `2r` and mass `2m`, are welded together and mounted on a frictionless axis through their common center. (a) What is the total moment of inertia of the two discs? (b) A light string is wrapped around the edge of the smaller disc and a block of mass `m_(0)` is suspended from the free end of the string. If the block is released from rest at a distance `h`, what is its speed just before it strikes the floor? |
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Answer» (`a`) `I_(1)=(1)/(2)mr^(2), I_(2)=(1)/(2)xx2mxx(2r)^(2)=4mr^(2)` `I=I_(1)+I_(2)=(9mr^(2))/(2)` (`b`) Loss in the gravitational potential of block `=` gain in the kinetic energy of (block `+` disc) `m_(0)gh=(1)/(2)m_(0)v^(2)+(1)/(2)Iomega^(2)` `v=romegaimplies omega= (v)/(r)` `=(1)/(2)m_(0)v^(2)+(1)/(2)xx(9mr^(2))/(2)xx(v^(2))/(r^(2))` `((1)/(2)m_(0)+(9)/(4)m)v^(2)=((2m_(0)+9m)/(4))v^(2)` `v=sqrt((4m_(0)gh)/(9m+2m_(0)))` |
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