Equilibrium: Practice Questions

Where is the centre of gravity of a uniform circular metal ring located?

The diagram shows a uniform bar of length \( 80\text{ cm} \) and weight \( 5.0\text{ N} \) pivoted at the \( 20\text{ cm} \) mark.
What weight must be hung at the \( 0\text{ cm} \) mark to keep the bar in horizontal equilibrium?

A non-uniform rod of length \( 100\text{ cm} \) and weight \( 30\text{ N} \) is balanced horizontally on a pivot at the \( 40\text{ cm} \) mark when a \( 20\text{ N} \) weight is placed at the \( 10\text{ cm} \) mark.
What is the distance of the rod's centre of gravity from the \( 0\text{ cm} \) mark?

According to the Principle of Moments, which condition must be met for a body to be in equilibrium?

A uniform rectangular block is placed on a rough plank. One end of the plank is slowly lifted to tilt the block.
At what point will the block topple over?

A rigid object is in equilibrium. According to the conditions for static equilibrium, the sum of the clockwise moments about any pivot must equal the sum of the anticlockwise moments about the same pivot. State the other condition that must be satisfied regarding the forces acting on the object.

A non-uniform rod of length \(1.0\text{ m}\) balances at the \(60\text{ cm}\) mark when no weights are attached. When the rod is supported by a pivot at the \(50\text{ cm}\) mark, it is balanced horizontally by a \(2.0\text{ N}\) weight placed at the \(0\text{ cm}\) mark. Calculate the weight of the rod.