99 Percentile Qs Bank for JEE MainPhysicsMechanical Properties of Solids
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
A. b^2 a 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 . Dividing Eq. (i) by Eq. (ii), we get Y₁ Y₂ = F₁ l₁ A₁ l₁ F₂ l₂ A₂ l₂ Force on steel wire from free body diagram T=F₁=(2 g) newton Force on brass wire from free body diagram F₂=T^ =T+2 g=(4 g) newton Now, putting the value of F₁, F₂ , in Eq. (iii), we get Y₁ Y₂ = ( 2 g 4 g ) ( r₂^2 r₁^2 ) [ l₁ l₂ ] ( l₂ l₁ ) or c= 1 2 ( 1 b^2 ) a ( l₂ l₁ ) or l₁ l₂ = ( a 2 b^2 c )