## Ruchi. 3 years ago a steel tape is calibrated at 20'c .on a cold day when the temperature is -15'c ,what will be percentage error in tape?

1. Ruchi.

@tanvidais13 @csaltos @uncle

2. Ruchi.

@HELLSGUARDIAN

3. HELLSGUARDIAN

whenever something is heated it expands & when cooled it contracts..so this case can be considered as the case of cooling..use equation $change \in length=- \alpha \Delta T L$ where L is original length ,$\Delta T$ is change in temperature..and $\alpha$ is coefficient of thermal expansion of steel.. when u have found the change in length the %ge error will be given as (change in length/original length)*100 can u do the calculations?

4. Ruchi.

hey i hav to find percentage error intape.

5. HELLSGUARDIAN

it will be change in length/original length*100

6. Ruchi.

bt length is nt mention only temp. is mention

7. HELLSGUARDIAN

L in this formula will be cancelled as it is in both numerator and denominator..

8. Ruchi.

hey cn u solve it i'm nt getting u?

9. HELLSGUARDIAN

wait for 5 minute then i will upload the solution

10. Ruchi.

okay

11. HELLSGUARDIAN

12. HELLSGUARDIAN

you get it?

13. Ruchi.

no

14. HELLSGUARDIAN

okay tell me where u have the doubt?

15. Ruchi.

change in length

16. 03225186213

orignal lenth is calibrated length and change is occur when measured at -15c

17. 03225186213

have u got it

18. Ruchi.

@UnkleRhaukus

19. Ruchi.

hey ash can u hlp me out

20. ash2326

Yes. Where do you have trouble understanding?

21. Ruchi.

i'm nt geting the percentage error

22. ash2326

All materials' length changes with temperature. Change in length is given as $\Delta L=\alpha \Delta T L$ Here $$\Delta T$$ is the change in temp. $$\alpha$$ is the linear coefficient of thermal expansion. Do you get this formula?

23. Ruchi.

yes,after put result answer is nt coming

24. ash2326

Let's find the change in length $$\alpha$$ for steel= $$10.8\times 10^{-6} / C$$ C= degree centigrade What's $$\Delta T$$ here?

25. Ruchi.

35

26. ash2326

it's -35. The length will decrease $\Delta T=(-15)-(20)=-35$

27. ash2326

$\text{now find}\ \Delta L \ \text{in terms of L}$

28. Ruchi.

29. ash2326

30. Ruchi.

YES

31. ash2326

Mind sharing here?

32. Ruchi.

its -0.042%

33. ash2326

Does you question mentions the value of alpha?

34. Ruchi.

no ur answer that u get

35. ash2326

It's because of the value of alpha. For steel it varies between $$11-13 *10^{(-6)} /C$$ Use $$12\times 10^{-6} /C$$ and you'd get the answer

36. ash2326

Do you get it?

37. rohit123

99.94%

38. Ruchi.

no .

39. Ruchi.

i think that if we use difference in reading we get the answer.in place of length

40. Ruchi.