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Four rods A, B, C and D are of the same ...

Four rods `A, B, C` and `D` are of the same length and material but of different radii `r, rsqrt(2),rsqrt(3)` 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

A

the stress in the rods are in the ratio 1 : 2 : 3 : 4

B

the force on the rod 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

Text Solution

Verified by Experts

The correct Answer is:
B, C
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Knowledge Check

  • Four rods A, B, C and 1 ) of the same length and material but of different radii r, rsqrt(2),rsqrt(3) 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

    A
    the stress in the rods `A, B, C` and `D` is 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 is in the ratio `1:2:3:4 `
    D
    it is independent of area like surface tension while friction depends

  • Two rods of different materials with coefficients linear thermal expansion alpha_(1), alpha_(2) , and Young's moduli Y_(1) and Y_(2) , respectively are fixed between two rigid walls. They are heated to have the same increase in temperature . If the rods do not bend and if alpha_(1) : alpha_(2) = 2 : 3 , then thermal stresses developed in the two rods will be equal when Y_(1) : Y_(2) ie equal to

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    D
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