please help **Problem #4**: A beam is machined to be bolted at the base and have a channel for routing cables. As shown in the figure below, the cross-sectional shape of the beam consists of a rectangular base under a square raised portion that has a semi-circular groove cut out of the top of it. The dimension of \( a \) for the machined beam is specified below. Determine:a) the centroid location, \( Y_c \), along the vertical \( Y_c \) axis.b) the moment of inertia, \( I_{Xc} \), about the centroidal \( x_c \) axis. ### Diagram Explanation:- The diagram shows the cross-sectional view of a beam and is divided into two main sections.- The bottom section is a rectangular base with a width of \( 5a \) and a height of \( a \).- The top section is a square raised portion with a height and width of \( 3a \), with a semi-circular groove cut out at the top.- The semi-circular groove has a radius of \( a \).- The overall dimensions of the structure in the figure include: - Width of the entire base: \( 5a \) - Height of the base: \( a \) - Height of the raised square portion without the groove: \( 3a \) - Width of the raised square portion: \( 3a \) - Location of \( Y_c \), marked along the vertical axis. - Location of \( X_c \), marked on the horizontal axis.**Parameters:**- \( a = 2.5 \, \text{cm} \)**Instructions:**- Enter the centroid location \( y_c \) in cm.

Problem #4. A beam is machined to be bolted at the base and have a channel for routing cables. As shown in the figure below, the cross sectional shape of the beam consists of a rectangular base under a square raised portion that has a semi-circular groove cut out of the top of it. The dimension of a for the machined beam is specified below. Determine: a) the centroid location, yc. along the vertical Yc axis. b) the moment of inertia, Ixc. about the centroidal xe axis. a 2.5 cm 3a a . 0.50 SR -0.50 20 301 So t Enter the centroid location y, in cm. TXC-

Problem #4. A beam is machined to be bolted at the base and have a channel for routing cables. As shown in the figure below, the cross sectional shape of the beam consists of a rectangular base under a square raised portion that has a semi-circular groove cut out of the top of it. The dimension of a for the machined beam is specified below. Determine: a) the centroid location, yc. along the vertical Yc axis. b) the moment of inertia, Ixc. about the centroidal xe axis. a 2.5 cm 3a a . 0.50 SR -0.50 20 301 So t Enter the centroid location y, in cm. TXC-

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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please help

**Problem #4**:

A beam is machined to be bolted at the base and have a channel for routing cables. As shown in the figure below, the cross-sectional shape of the beam consists of a rectangular base under a square raised portion that has a semi-circular groove cut out of the top of it. The dimension of \( a \) for the machined beam is specified below. Determine:

a) the centroid location, \( Y_c \), along the vertical \( Y_c \) axis.

b) the moment of inertia, \( I_{Xc} \), about the centroidal \( x_c \) axis.

### Diagram Explanation:

- The diagram shows the cross-sectional view of a beam and is divided into two main sections.
- The bottom section is a rectangular base with a width of \( 5a \) and a height of \( a \).
- The top section is a square raised portion with a height and width of \( 3a \), with a semi-circular groove cut out at the top.
- The semi-circular groove has a radius of \( a \).
- The overall dimensions of the structure in the figure include:
- Width of the entire base: \( 5a \)
- Height of the base: \( a \)
- Height of the raised square portion without the groove: \( 3a \)
- Width of the raised square portion: \( 3a \)
- Location of \( Y_c \), marked along the vertical axis.
- Location of \( X_c \), marked on the horizontal axis.

**Parameters:**
- \( a = 2.5 \, \text{cm} \)

**Instructions:**
- Enter the centroid location \( y_c \) in cm.

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Step 3: Calculation of the centroid location, yc along the vertical Yc axis.

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Step 4: Calculation of the moment of inertia, IXc about the centroidal Xc axis.

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