## Yahoo! 2 years ago Four rods of equal mass m each , Ab , BC , CA , DB are placed as shown. The moment of inertia of the system about B perpendicular to the plane ABC is (AB=a)

1. Yahoo!

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2. Yahoo!

@JamesJ

3. JamesJ

Obviously break down the problem rod by rod.

4. JamesJ

And if you're really stuck, you're just going to integrate rod by rod.

5. Yahoo!

I (BC) = ma^2/6 ryt ?

6. shubhamsrg

Its basically a maths ques, you just need to find rod lengths, after doing that you just have to calculate moment of inertia of each rod about B and add all

7. Yahoo!

Yup . i Have Calculated the length of rods BC = a/sqrt(2) , AC = a/sqrt(2) , DB = (sqrt2) * a / sqrt3

8. Yahoo!

I (BC) = ma^2/6 ryt ?

9. shubhamsrg

yep

10. Yahoo!

I (DB) = ma^2/18 ?

11. shubhamsrg

won' that be (2/9)ma^2

12. Yahoo!

Hw ?

13. shubhamsrg

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14. Yahoo!

I (DB) = M L^2 / 3 * sin^2 30 ryt ?

15. shubhamsrg

why sin ?

16. Yahoo!

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17. shubhamsrg

I don;t think angle matters

18. shubhamsrg

For calculation of I,

19. shubhamsrg

Because the axis is perpendicular to plane, the rod will make 90 degrees with the axis, doesn't matter how it is placed.

20. shubhamsrg

Do you have the final ans ?

21. Yahoo!

Yup 25 M a^2 / 18

22. shubhamsrg

<Lets see if we get that by my method>

23. shubhamsrg

So DB = 2M a^2 /9

24. shubhamsrg

And AC = ma^2/6 + 3ma^2/6 = 2ma^2 /3

25. shubhamsrg

So sum = ma^2 (2/3 + 2/9 + 1/6) = 19/18ma^2

26. shubhamsrg

hmm, okay doesn't match

27. Yahoo!

i think that angle matters

28. shubhamsrg

Wait I missed AB

29. shubhamsrg

AB = ma^2 /3 Sum = 25/18

30. shubhamsrg

Got it! B|

31. Yahoo!

But Hw Did u Claculate I (AC) ??

32. shubhamsrg

33. Yahoo!

Ok...got it....:)

34. shubhamsrg

"Angle will not matter here" ;)