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type=MCQ · page=24–25 · marks=2 · content_conf=0.7999999999999999 · math_conf=0.835

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file: GATE CH 2020 (with Solutions).pdf

pages: 24–25

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A hollow cylinder of equal length and inner diameter (i.e., L=D) is sealed at both ends with flat plate, as shown in the figure. Its inner surfaces A A and A radiate energy.

.

Options

A.
$F_2_1 = 2-1$
B.
$F_{21} = /frac{(2-1)}{2}$
C.
$F_{21} = /frac{(2-1)}{4}$
D.
$F_{21} = /frac{(2-1)}{8}$

Answer

Solution

.

Given, F₁ ₃=3 − 2 2 & L=D

F_{11}+F_{12}+F_{13} = 1

0+F_{12}+3-22 = 1

F_1_2 = 22-2

From Reciprocity theorem

A_1F_{12} = A_2F_{21} ⇒ F_{21} = /frac{A_1}{A_2} /times F_{12}

F_{21} = /frac{/\pi{}{}R^2}{2/\pi{}{}RL} /times (22-2)

F_{21} = /frac{/\pi{}{}R^2}{2/\pi{}{}R}(2R) /times (22-2)

F_{21} = /frac{(2-1)}{2}

Hence, the correct option is (B).

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Source PDF: GATE CH 2020 (with Solutions).pdf

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option_B	24	`—`	`—`none	`—`	`REVIEW`
option_C	24	`—`	`—`none	`—`	`REVIEW`
option_D	24	`—`	`—`none	`—`	`REVIEW`
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Dimensions

structurePASS
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optionsFAIL
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Issues

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option_D_operator_set_changed_raw_vs_derived