Question

Question: The moment of inertia of a surface about an axis through its centroid is 4200 mm. if the area of the surface is 100 mm?, what will be the moment of inertia about a parallel axis 6mm distance from the centroid? Option 1: 4200 mm4 Option 2: 600 mm4 Option 3: 3600 mm4 Option 4 7800 mm 4​

Answer 1

Answer:

2 is the right answer

Explanation:

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Answer 2

Option 4) 7800 $mm^{4}$ will be the moment of inertia about a parallel axis 6mm distance from the centroid.

Step-by-step explanation:

Moment of inertia is a measurable statistic of a body's rotational inertia—that is, the resistance that the body shows to having its rotation speed along an axis altered by the implementation of torque (turning force).

Given:

Centroid is 4200 mm

The area of the surface is 100 mm

To find:

To find the moment of inertia about a parallel axis 6mm distance from the centroid.

Formula used:

The following is the formula for the moment of inertia about such a parallel axis to the centroid:

$I_{XP} =I_{XC} +Ad^{2}$

Where,

$I_{XP}$ = moment of inertia about a parallel axis.

$I_{XC}$ = moment of inertia about the centroid.

A = surface area

d = distance between centroid and axis.

Solution:

Given,

$I_{XC}=4200mm^{4}$

$A=100mm^{2}$

$d=6mm$

Now substitute the given values in the formula $I_{XP} =I_{XC} +Ad^{2}$

$I_{XP} =4200 +100*(6)^{2}$

$I_{XP} =4300*36$

$I_{XP} =7800mm^{4}$

Hence, the moment of inertia about a parallel axis 6mm distance from the centroid is option(4) $7800mm^{4}$