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QJEEM19Ph54b5: JEE Main 2019 Physics - Class 11 JEEM19Ph54b5 Solution: A cylinder of radius R is surrounded by a cylindrical shell of…

A cylinder of radius R is surrounded by a cylindrical shell of inner radius R and outer radius 2R. The thermal conductivity of the material of the inner cylinder is K1 and the of the outer cylinder is K2. Assuming no loss of heat, the effective thermal conductivity of the system for heat flowing along the length of the cylinder is :

Multiple Choice Options

  • A K1 + K2
  • B K1+3K24{{{K_1} + 3{K_2}} \over 4}
  • C K1+K22{{{K_1} + {K_2}} \over 2}
  • D 2K1+3K25{{2{K_1} + 3{K_2}} \over 5}

Step-by-Step Verified Solution

JEE Main 2019 (Online) 12th January Morning Slot Physics - Heat and Thermodynamics Question 323 English Explanation
Keq = K1A1+K2A2A1+A2{{{K_1}{A_1} + {K_2}{A_2}} \over {{A_1} + {A_2}}}

= K1(πR2)+K2(3πR2)4πR2{{{K_1}\left( {\pi {R^2}} \right) + {K_2}\left( {3\pi {R^2}} \right)} \over {4\pi {R^2}}}

= K1+3K24{{{K_1} + 3{K_2}} \over 4}

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