KVPY2019PhysicsMechanical Properties of Solids
A metal rod of cross-sectional area 10 - 4   m 2 is hanging in a chamber kept at 20 ° C with a weight attached to its free end. The coefficient of thermal expansion of the rod is 2 . 5 × 10 - 6   K - 1 and its Young's modulus is 4 × 10 12   N / m 2 . When the temperature of the chamber is lowered to T , then a weight of 5000   N needs to be attached to the rod, so that its lengt
Options
- A15 ° C
- B12 ° C
- C5 ° C
- D0 ° C
Correct answer
A. 15 ° C
Step-by-step solution
Length of rod given remains unchanged. This means contraction due to cooling is equals to elongation due to hanging of weight. As, thermal strain = strain caused by weight ⇒ α Δ θ = Δ l l ⇒ Δ θ = Δ l / l α = F Y A α ∵ Y = F / A Δ l / l Note Δ θ in K is same as Δ θ in C ∘ . ∴ 20 - T = 5 ° C or T = 15 ° C