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

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 $I_x$ with respect to the $x$ axis is given by the integral of $y^2$ 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 $I_x$ with respect to the $x$ axis is: \[ I_{x} = \int y^{2} \, dA \]