Four rods \( A, B, C, D \) of same length and material but of different radii \( r, r \sqrt{2}, ...

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Four rods \( A, B, C, D \) of same length and material but of different radii \( r, r \sqrt{2}, r \sqrt{3} \) and \( 2 r \) respectively are held between two rigid walls. The temperature of all rods is increased by same amount. 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 \( 1: 2: 3: 4 \)
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