Question #107682

A rectangular brass bar of mass M has dimensions a,b,c. The moment of inertia I is given by

I = M(a squared + b squared)/12 and the following measurements are made:

M= 135.0 +/- 0.1 g

a= 80 +/- 1 mm

b= 10 +/- 1 mm

c= 20.00 +/- 0.1 mm

Calculate the standard error in

1) Density p of material

2) Moment of Inertia I

My answers:

1) 8,4375 * 10 ( to the power -6)

2) Inertia I got 73,125 kg.m (squared) and standard error i struggled with.

Please assist and confirm whether or not my answers are correct.

I = M(a squared + b squared)/12 and the following measurements are made:

M= 135.0 +/- 0.1 g

a= 80 +/- 1 mm

b= 10 +/- 1 mm

c= 20.00 +/- 0.1 mm

Calculate the standard error in

1) Density p of material

2) Moment of Inertia I

My answers:

1) 8,4375 * 10 ( to the power -6)

2) Inertia I got 73,125 kg.m (squared) and standard error i struggled with.

Please assist and confirm whether or not my answers are correct.

Expert's answer

1)

"\\frac{\\Delta \\rho}{\\rho}=\\frac{1}{80}+\\frac{1}{10}+\\frac{0.1}{20}+\\frac{0.1}{135}=0.11824"

"\\rho=\\frac{m}{abc}=\\frac{0.135}{(0.08)(0.01)(0.02)}=8437.5\\frac{kg}{m^3}"

"\\Delta\\rho=8437.5(0.11824)=1000\\frac{kg}{m^3}"

2)

"\\frac{\\Delta I}{I}=2\\frac{\\Delta a}{a}+2\\frac{\\Delta b}{b}+\\frac{\\Delta m}{m}"

"\\frac{\\Delta I}{I}=2\\frac{1}{80}+2\\frac{1}{10}+\\frac{0.1}{135}=0.22574"

"\\Delta I=(0.22574)7.3125\\cdot 10^{-5}=2\\cdot 10^{-5}\\ kgm^2"

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