Questions: Multiple Choice Question The moment of inertia, Ix of an area A with respect to the x axis is given by the equation .
Ix=∫x dA
Ix=∫y^2 dA
Ix=∫y dA
Ix=∫x^2 dA
Transcript text: Multiple Choice Question
The moment of inertia, $I_{x}$ of an area $A$ with respect to the $x$ axis is given by the equation $\qquad$ .
$I_{x}=\int x d A$
$I_{x}=\int y^{2} d A$
$I_{x}=\int y d A$
$I_{x}=\int x^{2} d A$
Solution
Solution Steps
Step 1: Understanding the Moment of Inertia
The moment of inertia of an area with respect to an axis is a measure of how the area is distributed relative to that axis. For the x axis, it involves the distribution of the area in the y direction.
Step 2: Identifying the Correct Formula
The moment of inertia Ix with respect to the x axis is given by the integral of y2 times the differential area dA. This is because the distance from the x axis to a point in the area is given by the y coordinate.
Step 3: Selecting the Correct Option
Among the given options, the correct formula for the moment of inertia Ix with respect to the x axis is:
Ix=∫y2dA