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two wire of equal length and cross sectional area are suspended as shown in Figure. Their Youngs modulii are Y1=2 *10¹¹ Pa and Y2 =0.90 *10¹¹ Pa respectively. what will be the equivalent Youngs modulus of combination

two wire of equal length and cross sectional area are suspended as shown in Figure. Their Youngs modulii are Y1=2 *10¹¹ Pa and Y2 =0.90 *10¹¹ Pa respectively. what will be the equivalent Youngs modulus of combination

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Grade:12

2 Answers

Vikas TU
14149 Points
7 years ago
From RBD concept and eqm. balance Tensions in respective strings are mg/2 in both.
.i.e. 
T1 =mg/2 =T2
 
Total strain will be constant.
strain = s1 + s2
stress/Y = stress1/Y1 + stress/Y2
(T1 +T2)/AY = T1/AY1  +T2/AY2
Put  the values of Tension force,
mg/Y = mg/2Y1 + mg/2Y2
1/Y = 1/2Y1 + 1/2Y2
Put Y1 and Y2 and get the ansswer therfore.
Kushagra Madhukar
askIITians Faculty 628 Points
3 years ago
Dear student,
Please find the attached solution to your problem.
 
 
From RBD concept and eqm. balance Tensions in respective strings are mg/2 in both.
.i.e. 
T1 =mg/2 =T2
 
Total strain will be constant.
strain = s1 + s2
stress/Y = stress1/Y1 + stress/Y2
(T1 +T2)/AY = T1/AY1  +T2/AY2
Put  the values of Tension force,
mg/Y = mg/2Y1 + mg/2Y2
1/Y = 1/2Y1 + 1/2Y2
Hence, 1/Y = 29 x 10-11/36
Hence, Y = 1.2414 x 1011 Pa
 
Hope it helps.
Thanks and regards,
Kushagra

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