Four rods A, B, C and D of the same length and material but of different radii r, r $\sqrt{2}$ , r $\sqrt{3}$ and 2r respectively are held between two rigid walls. The temperature of all rods is increased through the same range. If the rods donot bend, then
a) The stress in the rods A, B, C 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 are 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

see full answer

High-Paying Jobs That Even AI Can’t Replace — Through JEE/NEET

🎯 Hear from the experts why preparing for JEE/NEET today sets you up for future-proof, high-income careers tomorrow.

An Intiative by Sri Chaitanya

only a

Both b and d

Both b and c

only d

answer is C.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

Thermal stress developed when rods of same materials and length are fixed between two rigid support is $Yα ∆ t$ which is independent of area but force developed is stress $\times$ area( $π r^{2}$ )

so force is proportional to r².

energy stored is

$\frac{{(s t r e s s)}^{2}}{2 Y} v o l u m e$

As lengths are same volume is proportional to area hence energy is also proportional to area ( $π r^{2}$ )

Hence the correct answers are both b and c.

Watch 3-min video & get full concept clarity

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Online Course for IIT JEE

Best Online Course for NEET

Best Online Course for CBSE

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Get Expert Academic Guidance – Connect with a Counselor Today!

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Online Course for IIT JEE

Best Online Course for NEET

Best Online Course for CBSE