Question

A force of 200 N is applied at one end of a wire of length 2 m and having area of cross-section 10^–2 cm², the other end of the wire is rigidly fixed. If of linear expansion of the wire α = 8 × 10^–6 / °C and young's modulus Y = 2.2 × 10¹¹(N / m²) and its temperature is increased by 5°C then the increase in the tension of the wire will be........... 

(A) 4.2 N 

(B) 4.4 N 

(C) 2.4 N 

(D) 8.8 N

Answer 1

Correct option: (D) 8.8 N

Explanation:

Force i.e. Tension in the wire = [{YAℓ} / L] = [(YAαLθ) / L] = YAαθ 

where Y = Young's modulus 

A = area 

α = coefficient of linear expansion 

θ = Increase in temperature 

∴ Tension = 2.2 × 10¹¹ × 10^–2 × 10^–4 × 8 × 10^–6 × 5 

= 8.8 N