Question

Is the center of gravity assigned at the right place for the following bodies?

Answer 1

The center of gravity for a body is typically assigned at the right place, which is the point where the entire weight of the body can be considered to act. This point is crucial for analyzing the body's stability and equilibrium.

Step-by-step explanation:

The center of gravity (CoG) is the point where the entire weight of an object can be considered to be concentrated. For a uniform density object with a regular shape, the CoG is often at the geometric center, like the midpoint of a symmetrical object. However, for irregularly shaped or asymmetric bodies, determining the center of gravity may involve more complex calculations.

In mathematical terms, the center of gravity
`(\(x_{\text{CoG}}\))` for a one-dimensional object can be found using the formula
`\(x_{\text{CoG}} = (\sum_(i) m_i \cdot x_i)/(\sum_(i) m_i)\)`, where \(m_i\) is the mass of the ith particle and
`\(x_i\)` is its position. For a two-dimensional object, the formula becomes
`\(x_{\text{CoG}} = (\sum_(i) m_i \cdot x_i)/(\sum_(i) m_i)\) and \(y_{\text{CoG}} = (\sum_(i) m_i \cdot y_i)/(\sum_(i) m_i)\)`. These calculations ensure that the CoG accurately represents the distribution of mass within the object.

In engineering and physics, assigning the center of gravity at the right place is crucial for predicting how an object will behave under the influence of external forces, ensuring proper balance, stability, and safety.