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Question

Two cylinders of same material and of same length are joined to end as shown in figure. The upper end of A is rigidly fixed. Their radii are in ratio of 1 : 2, If the lower end of B is twisted by an angle theta comma blankthe angle of twist of cylinder A is

  1. fraction numerator 15 over denominator 16 end fraction theta    
  2. fraction numerator 16 over denominator 15 end fraction theta    
  3. fraction numerator 16 over denominator 17 end fraction theta    
  4. fraction numerator 17 over denominator 16 end fraction theta blank    

The correct answer is: fraction numerator 16 over denominator 17 end fraction theta


    For cylinder A,
    tau equals fraction numerator pi eta r to the power of 4 end exponent over denominator 2 l end fraction theta to the power of ´ end exponent
    For cylinder B comma blank tau equals blank fraction numerator pi eta open parentheses 2 r close parentheses to the power of 4 end exponent left parenthesis theta minus theta to the power of ´ end exponent right parenthesis over denominator 2 l end fraction
    fraction numerator pi eta r to the power of 4 end exponent theta to the power of ´ end exponent over denominator 2 l end fraction equals blank fraction numerator pi eta open parentheses 2 r close parentheses to the power of 4 end exponent left parenthesis theta minus theta to the power of ´ end exponent right parenthesis over denominator 2 l end fraction
    theta to the power of ´ end exponent equals fraction numerator 16 over denominator 17 end fraction blank theta

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