Explain why some solids float and others sink, and describe an experiment to find the density of iron.

• Density: A solid floats if its density is less than the density of water ($\rho_{solid} < \rho_{water}$). It sinks if its density is greater than the density of water ($\rho_{solid} > \rho_{water}$).
• Upthrust: When a solid is immersed in water, it experiences an upward buoyant force (upthrust). If this upthrust is greater than or equal to the weight of the solid, it floats. If the upthrust is less than the weight of the solid, it sinks.

Apparatus: Electronic balance, measuring cylinder, water, piece of iron, thread.
Procedure:

1. Use the electronic balance to measure the mass ($m$) of the piece of iron. Record this value.
2. Pour a suitable amount of water into the measuring cylinder and record the initial volume ($V_1$).
3. Gently lower the piece of iron into the measuring cylinder using a thread until it is fully submerged. Ensure no air bubbles are trapped.
4. Record the new volume ($V_2$) of water in the measuring cylinder. Measurements to be made: Mass of iron ($m$), initial volume of water ($V_1$), final volume of water and iron ($V_2$). How to obtain a conclusion: The volume of the iron piece ($V$) is calculated as the difference between the final and initial volumes: $V = V_2 - V_1$. The density ($\rho$) of the iron piece is then calculated using the formula:

Precaution taken:

• Ensure the piece of iron is fully submerged in the water.
• Read the measuring cylinder at eye level to avoid parallax error.
• Ensure the electronic balance is zeroed before measuring the mass.

• A high density: Ship's anchor (to ensure it sinks and holds position).
• A low density: Life jacket (to provide buoyancy and help a person float).

• Weight (W): Acting vertically downwards from the center of the bob.
• Tension/Restoring force (T): Acting vertically upwards along the rubber band, from the rubber band to the bob.

• Rubber band: Elastic potential energy (due to its stretched state).
• Bob: Gravitational potential energy (due to its height above a reference point).

Justification: Hooke's Law states that the force applied is directly proportional to the extension produced, provided the elastic limit is not exceeded. This implies a linear relationship between force and extension. However, some elastic materials, such as rubber, do not exhibit a linear force-extension graph. While they are elastic and return to their original shape after deformation, the relationship between force and extension is non-linear, especially at larger extensions.

• In section OA: The car starts from rest and its velocity increases uniformly from 0 m/s to 5 m/s over 10 seconds. This indicates that the car is undergoing uniform acceleration.
• In section AB: The car's velocity remains constant at 5 m/s from 10 seconds to 20 seconds. This indicates that the car is moving with uniform velocity (zero acceleration).

The distance covered is the area under the velocity-time graph.
The graph consists of a triangle (OA) and a rectangle (AB).