Rotation 5 Question 30

42. A carpet of mass M made of inextensible material is rolled along its length in the form of a cylinder of radius R and is kept on a rough floor. The carpet starts unrolling without sliding on the floor when a negligibly small push is given to it. Calculate the horizontal velocity of the axis of the cylindrical part of the carpet when its radius reduces to R/2.

(1990,8M)

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Answer:

Correct Answer: 42. v=14Rg3

Solution:

  1. Let M be the mass of unwound carpet. Then,

M=MπR2πR22=M4

From conservation of mechanical energy :

MgRMgR2=12M4v2+12Iω2

or MgRM4gR2=Mv28+1212×M4×R24vR/2

or 78MgR=3Mv216

v=14Rg3

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