Physics
Fluid-Mechanics
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A metal cylinder of mass m and radius R1 moves down vertically in a pipe of radius R2  as shown open parentheses R subscript 2 minus R subscript 1 close parentheses is very small. There is a liquid between the cylinder and pipe whose coefficient of viscosity is eta. If the cylinder moves down with a constant velocity v, the value of eta is (length of the cylinder = L).

  1. fraction numerator m g open parentheses R subscript 2 minus R subscript 1 close parentheses over denominator pi R subscript 2 L v end fraction
  2. fraction numerator m g open parentheses R subscript 2 minus R subscript 1 close parentheses over denominator 2 pi R subscript 2 L v end fraction
  3. fraction numerator m g open parentheses R subscript 2 minus R subscript 1 close parentheses over denominator pi R subscript 1 L v end fraction
  4. fraction numerator m g open parentheses R subscript 2 minus R subscript 1 close parentheses over denominator 2 pi R subscript 1 L v end fraction

The correct answer is: fraction numerator m g open parentheses R subscript 2 minus R subscript 1 close parentheses over denominator 2 pi R subscript 1 L v end fraction


    eta 2 pi R subscript 1 L fraction numerator left parenthesis v minus 0 right parenthesis over denominator open parentheses R subscript 2 minus R subscript 1 close parentheses end fraction equals m g semicolon eta equals fraction numerator m g open parentheses R subscript 2 minus R subscript 1 close parentheses over denominator 2 pi R subscript 1 L v end fraction

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