MHT CET2017PhysicsMechanical Properties of Solids
A metal rod of length L and cross-sectional area A is heated through T ° C . What is the force required to prevent the expansion of the rod lengthwise? [Y = Young's modulus of the material of rod, α = coefficient of linear expansion ]
Options
- AY A α T ( 1 - α T )
- BY A α T ( 1 + α T )
- C( 1 - α T ) Y A α T
- D( 1 + α T ) Y A α T
Correct answer
B. Y A α T ( 1 + α T )
Step-by-step solution
∆ L = α L T ...... (i) Also Y = F A . L ( 1 + α t ) ∆ L Or ∆ L = F . L ( 1 + α t ) A . Y ........ (ii) Equating (i) and (ii) F . L 1 + α t A . Y = α L T ∴ F = A Y α T ( 1 + α t )