Answer :
Answer:
The ratio of the moment of inertia through the second axis to the moment of inertia through the first axis is 1.48.
Explanation:
Given that,
Length of rod = 100 cm
The first axis passes through the 50-cm mark and the second axis passes through the 30-cm mark.
We need to calculate the moment of inertia when the axis passing through
Using formula of moment of inertia
[tex]I_{1}=\dfrac{1}{12}ml^2[/tex]
Put the value into the formula
[tex]I_{1}=\dfrac{1}{12}m\times(1\times10^{-2})^2[/tex]
We need to calculate the distance from center of mass
[tex]x=50-30= 20 cm[/tex]
We need to calculate the moment of inertia when the axis passing through
Using formula of moment of inertia
[tex]I_{2}=I_{1}+mx^2[/tex]
Put the value into the formula
[tex]I_{2}=\dfrac{1}{12}m\times(1\times10^{-2})^2+m\times(20\times10^{-2})^2[/tex]
[tex]I_{2}=m(\dfrac{1}{12}\times(1.00)^2+(0.2)^2)[/tex]
[tex]I_{2}=m(\dfrac{1}{12}+0.04)[/tex]
We need to calculate the ratio of the moment of inertia through the second axis to the moment of inertia through the first axis
Using formula of ration of moment of inertia
[tex]\dfrac{I_{2}}{I_{1}}=\dfrac{m\times\dfrac{1.48}{12}}{\dfrac{1}{12}m\times(1\times10^{-2})^2}[/tex]
[tex]\dfrac{I_{2}}{I_{1}}=1.48[/tex]
Hence, The ratio of the moment of inertia through the second axis to the moment of inertia through the first axis is 1.48.