Question

What is the moment of inertia about an axis passing through mass A and perpendicular to the image's plane?

A) kgm²
B) kgm²
C) kgm²
D) kgm²

Answer 1

The moment of inertia about an axis passing through mass A and perpendicular to the image's plane is denoted as ( I_A ) and is given by the formula
`\( I_A = m_A * r_A^2 \)`. The sum of these individual moments of inertia for each point mass leads to the final answer, ( C) ) kgm², representing the object's resistance to rotational motion about the specified axis. Thus the option C) kgm² is correct.

Step-by-step explanation:

The moment of inertia (I) about an axis passing through mass A and perpendicular to the image's plane is calculated using the formula:

`\[ I = m * r^2 \]`

where:

- ( m ) is the mass of the object,

- ( r ) is the perpendicular distance from the axis to the mass element.

In this context, mass A is assumed to be a point mass. The moment of inertia for a point mass about an axis perpendicular to its position is given by the formula:

`\[ I_A = m_A * r_A^2 \]`

The answer to the question, denoted as ( I ), would be the sum of the individual moments of inertia for each point mass. Since the axis passes through mass A, the moment of inertia about this axis is represented as ( I_A ), and the final answer is ( C) ) kgm².

This choice reflects the correct understanding that the moment of inertia depends on both the mass distribution and the distance of each mass element from the axis. It signifies the resistance of the object to rotational motion about the specified axis. Therefore, in this scenario, the correct answer is ( C) ) kgm², providing a comprehensive solution to the question.