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Q.

Two rods of different materials and identical cross sectional area, are joined face to face at one end and their free ends are fixed to the rigid walls. If the temperature of the surroundings is increased by 30°C, the magnitude of the displacement of the joint of the rod is (length of rods l1=l2=1unit, ratio of their young's moduli, Y1/Y2=2, coefficients of linear expansion are α1 and α2)

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a

5α2−α1

b

10α1−α2

c

10α2−2α1

d

52α1−α2

answer is C.

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Detailed Solution

Y1( Strain )1=Y2( Strain )2Y1a1lΔT1−xl=Y2a2lΔT2+xl Displacement of the rod x=Y2a2−Y1a1Y1+Y2×l×ΔT
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Two rods of different materials and identical cross sectional area, are joined face to face at one end and their free ends are fixed to the rigid walls. If the temperature of the surroundings is increased by 30°C, the magnitude of the displacement of the joint of the rod is (length of rods l1=l2=1unit, ratio of their young's moduli, Y1/Y2=2, coefficients of linear expansion are α1 and α2)