Refer to Exercise 5.a. Assume g = 9.80 m/s2 exactly, and

Chapter 3, Problem 15E

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QUESTION:

Refer to Exercise 5.

a. Assume \(g=9.80 \mathrm{~m} / \mathrm{s}^{2}\) exactly, and that \(L=0.855 \pm 0.005 \mathrm{~m}\). Estimate T , and find the relative uncertainty in the estimate.

b. Assume \(L=0.855 \mathrm{~m}\) exactly, and that \(T=1.856 \pm 0.005 \mathrm{~s}\). Estimate g, and find the relative uncertainty in the estimate.

Equation Transcription:

Text Transcription:

g=9.80 m/s^2

L=0.855{+/-}0.005 m

L=0.855 m

T=1.856{+/-}0.005 s

Questions & Answers

QUESTION:

Refer to Exercise 5.

a. Assume \(g=9.80 \mathrm{~m} / \mathrm{s}^{2}\) exactly, and that \(L=0.855 \pm 0.005 \mathrm{~m}\). Estimate T , and find the relative uncertainty in the estimate.

b. Assume \(L=0.855 \mathrm{~m}\) exactly, and that \(T=1.856 \pm 0.005 \mathrm{~s}\). Estimate g, and find the relative uncertainty in the estimate.

Equation Transcription:

Text Transcription:

g=9.80 m/s^2

L=0.855{+/-}0.005 m

L=0.855 m

T=1.856{+/-}0.005 s

ANSWER:

Answer:

Step 1 of 3:

         a). The aim is to estimate T and to find the relative uncertainty in T.

               Given,  and  

                    Here,  L = 0.855,

                  Now, estimate the value of is

                            

   

                               

                            = 6.28 (0.2953)

                             = 1.856 s

             Then, differentiate with respect to , we get

                      

                                  =                     (since

                           

 

     

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