## thushananth01 2 years ago A uniform steel wire X and Y, suspended at the same horizontal level, are connected by a light and cross-sectional area A, A weight of 30 N is placed at O, on the road OX : OY = 1 : 2. Both wires are stretched and the rod XY then remains horizontal. If he wire X has a young modulus E1 of 1.0 * 10^11 pa, calculate the yound modulus of E2 of the wire Y assuming the elastic limit is not exceeded for both wires.

1. thushananth01

|dw:1358779489492:dw|

2. thushananth01

@Hero @Preetha @ghazi @AravindG

3. AravindG

I think I saw a similiar question in NCERT text chapter 11 under topic of Young's modulus and all..take a look

4. thushananth01

can u give me the link of the book?

5. AravindG

you are not from India?

6. thushananth01

nope

7. AravindG

i suggest you google it..its easy to get NCERT CLASS 11 PHYSICS PART 2

8. thushananth01

do they have the solutions

9. AravindG

yes i think .....

10. AravindG

worth checking

11. AravindG

infact the book is very nice for reference

12. thushananth01
13. AravindG
14. thushananth01

can u change the language?

15. AravindG

ofcourse eng is below scroll down

16. AravindG

gt it?

17. thushananth01

the question isnt there

18. Mashy

Ok.. so since the xy is horizontal.. it means after stretching, both the bars have exactly the same length.. so i can say \[l1+\Delta l1 = l2 + \Delta l2 \] next step we find the stress that is coming on each of them.. that should be easy.. since the ration of ox: oy is given to us..

19. thushananth01

can u show the working please:)

20. Mashy

try doing it :P.. first you tell me how much will be the stress that comes on X and Y ?

21. thushananth01

stress = force/ area how do i distrbte the force

22. Mashy

first find the force.. force equals the weight that each one would experience.. the weight is at a ratio of 2:1 .. hence the distribution will be in inverse ratio right? 1:2.. cause if weight is far away, its effect is smaller!

23. Mashy

hence Fx : Fy = 2:1

24. Mashy

so now calculate Fx and Fy

25. thushananth01

Fx = 2/3 Fy Fy = 1/3 Fx ?

26. Mashy

total force is known to you.. so find the ratios now!

27. Mashy

Fx = 2/3 Ftotal :P and Fy = 1/3 Ftotal

28. thushananth01

Fx = 20N and Fy = 10N

29. Mashy

ok.. :D.. next.. find the stress on X and since young's modulus of X is given.. find the strain.. Similarly do the same thing for Y.. but young's modulus is not given.. divide the two equations to get rid of A

30. thushananth01

thanks alot Strain = F/A*E1 strain in X = 20/A* 1.0 * 10^11 strain is equal so E2 = stress/ strain E2 = 10/A *A*1.0*10^11/20 E2 = 5 * 10^11 pa

31. Mashy

woah wait.. how did you get the strain for Y ?

32. thushananth01

arent they equal

33. Mashy

nope :-/.. why would the strains be equal?

34. thushananth01

same mterial

35. Mashy

now you have to use the first equatoin.. that i put.. but use lx and ly notation instead of l1 and l2 notation

36. Mashy

they are NOT SAME MATERIAL.. IF THEY WERE.. THEY WOULD HAVE SAME YOUNG"S MODULUS :P

37. thushananth01

i dont undrstnd >< cn u shw the working

38. Mashy

use the first equation .. try doing it.. see you need to get rid of \[\Delta ly/ ly\] in that equation i asked you to build by dividing the two equations

39. Mashy

so here are the two equations \[Fx / Fy = Ex \Delta x ly / Ey \Delta ylx \] and \[lx + \Delta x = ly + \Delta y\] somehow use them

40. thushananth01

ok il use thnks fr ur help :)

41. Mashy

No problimo amigo :D