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Two rods (one semi-circular and other st...

Two rods (one semi-circular and other straight) of same material and of same cross-sectional area are joined as shown in the figure. The point A and B are maintained at different temperature. Find the ratio of the heat transferred through a cross-section of a semi-circular rod to the heat transferred through a cross section of the straight rod in a given time.

A

`2:pi`

B

`1:2`

C

`pi:2`

D

`3:2`

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(a) Three rod of lengths 20 cm each and area of cross-section 1 cm^(2) are joined to form a triangle ABC . The conductivities of the rods are K_(AB) = 50 J//m-s-.^(@)C, K_(BC) = 200 J//m-s-.^(@)C and K_(AC) = 400 J//m-s-.^(@)C . The junctions A, B and C are maintained at 40^(@)C , 80^(@)C and 80^(@)C respectively. Find the rate of heat flowing through the rods AB, AC and BC . (b) A semicircular rod is joineted as its end to a straight rod of the same material and the same cross-sectional area. The straight rod forms a diameter of the other rod. The junctions are maintained at different temperatures. Find the ratio of the heat transferred through a cross-section of the simicircular rod to the heat transferred through a cross-section of the straight rod in a given time.

A semicircular rods is joined at its end to a straight rod of the same material and the same cross-sectional area. The straight rod formss a diameter of the other rod. The junction are maintaine dat different temperature. Find the ratio of the heat transffered through a cross section of the straigh rod in a given time.

Knowledge Check

  • Two rods one is semi circular of thermal conductivity K_(1) and otheir is straight of thermal conductivity K_(2) and of same cross sectional area are joined as shown in the The points A and B are maintained at same temperature difference. If rate of flow of heat is same in two rods then K_(1)//K_(2) is .

    A
    `2:pi`
    B
    `1:2`
    C
    `pi:2`
    D
    `3:2`

  • A metal rod of length 2 m has cross sectional areas 2 A and A as shown in figure. The ends are maintained at temperatures 100° C and 70° C . The temperature at middle point C is

    A
    `80^(@)C`
    B
    `85^(@)C`
    C
    `90^(@)C`
    D
    `95^(@)C`

  • A uniform cylindrical rod of length L and cross-sectional area by forces as shown in figure. The elongation produced in the rod is

    A
    `(3F L)/(8 AY)`
    B
    `(3FL)/(5AY)`
    C
    `(8FL)/(3AY)`
    D
    `(5FL)/(3AY)`

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