AP EAMCET201922 Apr 2019Morning ShiftPhysicsMechanical Properties of SolidsActual
Two wires of equal length and equal cross sectional areas are suspended as shown in the figure. Their Young's modulii are (Y₁ ) and (Y₂ ), respectively. The equivalent Young's modulus is
Options
- A(Y₁+Y₂ )
- B( Y₁+Y₂ 2 )
- C( Y₁ Y₂ Y₁+Y₂ )
- D( Y₁ Y₂ )
Correct answer
B. ( Y₁+Y₂ 2 )
Step-by-step solution
Given, two wires have same length and equal cross-sectional area. i.e., (l₁=l₂=l ) and (A₁=A₂=A ) Suppose, (m ) is the mass of the hanging load. From figure, (2 T=m g ) i.e., (T= m g 2 ) Hence, stress on each wire (= T A = m g 2 A ) ( Y₁= stress strain = m g 2 A l l = m g l 2 A l )...(i) and (Y₂= stress strain = m g 2 A l l = m g l 2 A l )...(ii) If (Y ) be the equivalent Young's modulus of the combination, then, ( Y= m g l A l )...(iii) From Eqs. (i), (ii) and (iii), we get (Y= Y₁+Y₂ 2 )