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Physics-

General

Easy

Question

The twisting couple per unit twist for a solid cylinder of radius 3 cm is 0.1 N-m. The twisting couple per unit twist, for a hollow cylinder of same material with outer and inner radius 5 cm and 4 cm respectively will be

0.1 N-m
0.455 N-m
0.91 N-m
1.82 N-m

The correct answer is: 0.455 N-m

Twisting coupler per unit twist for solid cylinder, for hollow cylinder, $C subscript 1 end subscript equals fraction numerator pi eta r to the power of 4 end exponent over denominator 2 l end fraction$
$therefore blank C subscript 2 end subscript equals C subscript 1 end subscript fraction numerator r subscript 2 end subscript superscript 4 end superscript minus r subscript 1 end subscript superscript 4 end superscript over denominator r to the power of 4 end exponent end fraction equals fraction numerator 0.1 blank cross times open parentheses 5 to the power of 4 end exponent minus 4 to the power of 4 end exponent close parentheses over denominator partial differential to the power of 4 end exponent end fraction equals fraction numerator 36.9 over denominator 81 end fraction$
= 0.455 Nm

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