NEET2012PhysicsMechanical Properties of SolidsActual
If the ratio of lengths, radii and Young's modulus of steel and brass wires shown in the figure are a, b and c respectively, the ratio between the increase in lengths of brass and steel wires would be
Options
- Ab^2 a 2 c
- Bb c 2 a^2
- Cb a^2 2 c
- Da 2 b^2 c
Correct answer
D. a 2 b^2 c
Step-by-step solution
Free body diagram of the two blocks are Given, l₁ l₂ =a, r₁ r₂ =b, Y₁ Y₂ =c Let Young's modulus of steel is Y₁ and of brass is Y₂ Y₁= F₁ l₁ A₁ l₁ ...(i) and Y₂= F₂ l₂ A₂ l₂ ...(ii) Dividing Eq. (i) by Eq. (ii), we get Y₁ Y₂ = F₁ l₁ A₁ l₁ F₂ l₂ A₂ l₂ or Y₁ Y₂ = F₁ A₂ l₁ l₂ F₂ A₁ l₂ l₁ ...(iii) Force on steel wire from free body diagram T=F₁=2 g ~N Force on brass wire from free body diagram F₂=T^ =T+2 g=4 ~g ~N Now, putting the values of F₁, F₂ in Eq. (iii), we get Y₁ Y₂ = ( 2 g 4 g ) ( r₂^2 r₁^2 ) [ l₁ l₂ ] ( l₂ l₁