91Ó°ÊÓ

Relative density, often known as specific gravity, is a dimensionless number that indicates how dense a substance is compared to a reference substance—typically water for liquids and solids. It reveals how much heavier or lighter a material is in comparison to water.

For example, in this problem, the silver has a relative density of 10. This means silver is 10 times denser than water. On the other hand, the liquid in which the silver block is submerged has a relative density of 0.72. This means the liquid is less dense than water by 28% (1 - 0.72).

The calculation is usually expressed as, relative density = \(\frac{\text{density of substance}}{\text{density of reference}}\). Since the density of water is 1 g/cm³ or 1000 kg/m³, we often use this as a standard reference for solids and liquids.

Tension in the string refers to the force applied along the string that keeps the silver block suspended in the liquid. It is essentially the force required to counteract both the weight of the block and any upward buoyant force experienced by the block when submerged.

In this problem, to find the tension, you subtract the buoyant force from the weight of the block:

• The weight of the silver block is the force due to gravity: \(W = m \times g = 4 \text{ kg} \times 9.8 \text{ m/s}^2 = 39.2 \text{ N}\).
• The buoyant force, calculated earlier, equals 282.24 N acting upwards.

Then, the tension in the string is calculated by, \(T = W - F_b = 39.2 \text{ N} - 282.24 \text{ N} = -243.04 \text{ N}\).
This negative outcome suggests that if actual conditions hold, the setup needs adjustment, likely resulting in buoyancy making the block naturally float or requiring it to be restrained in some way.

Buoyant force is an upward force exerted by a fluid on a submerged object. This is the principle that allows objects to float or rise in fluids and is described by Archimedes' Principle. According to this principle, the upward buoyant force is equal to the weight of the fluid displaced by the object.

In the given exercise, the buoyant force can be calculated using the volume of the block and the density of the liquid. With the formula:

• Buoyant Force \(F_b = V_{silver} \times \rho_{liquid} \times g\)

Each variable is:

• \(V_{silver} = 0.4 \text{ m}^3\), as earlier calculated
• \(\rho_{liquid} = 720 \text{ kg/m}^3\) (density from relative density of 0.72)
• \(g = 9.8 \text{ m/s}^2\) (acceleration due to gravity)

Plugged into the formula, this gives a buoyant force of 282.24 N, demonstrating that the liquid exerts a significant upward force on the block as it attempts to displace liquid equal to its volume.