Grade 12Mechanics

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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Jayesh Mahajan

10 Years agoGrade 12

2 Answers

Vikas TU

10 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

5 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 10¹¹Pa

Hope it helps.

Thanks and regards,

Kushagra

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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

Jayesh Mahajan

2 Answers

Vikas TU

Kushagra Madhukar

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