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Q.

Four rods, ABC and D of the same length and material but of different radii r , r2,r3 and 2r respectively are held between two rigid walls. The temperature of all rods is increased through the same range. If the rods do not bend, then

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a

the stress in the rods A,BC and D are in the ratio 1:2:3:4

b

the forces on them exerted by the wall are in the ratio 1:2:3:4

c

the energy stored in the rods due to elasticity are in the ratio 1:2:3:4

d

the strains produced in the rods are in the ratio 1:2:3:4

answer is B, C.

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Detailed Solution

(b, c)

             F = YαTA = YαTπr2           So F r2            F1:F2: F3:F4  = 1:2:3:4

Energy stored = 12Fx = 12F×FlAY = F2l2πr2Y

Therefore energy stored r2

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