Stainless steel is an alloy of iron, chromium and nickel! A piece of stainless steel consists of 70% iron, 20% chromium and 10% nickel by volume - Leaving Cert Applied Maths - Question 9 - 2012

Let the length of the immersed part of the rod be x. Based on Archimedes' principle, the weight of the liquid displaced (which equals the weight of the rod) must balance the weight of the rod:

The buoyant force, B, can be expressed as:

$B = x imes 0.9 imes g$

Where 0.9 is the relative density of the liquid. However, since it is given:

$B = 0.756W$

Setting these equal gives:

$0.756 W = x imes 0.9 g$

For equilibrium:

W imes ext{sin} heta = B = x imes (2 - rac{x}{2}) imes g

Rearranging this gives:

$W imes 2 - W imes x = 0.756 W imes 0.9$

Using the given dimensions:

$x^2 - 4x + 336 = 0$

Solving the quadratic equation for x yields:

$x = 1.2 ext{ m}$.

Using the relationship:

ext{cos} θ = rac{0.4}{2 - 1} = rac{0.4}{1}

This simplifies to:

$ext{cos} θ = 0.4$

Thus, the angle θ is calculated as:

$θ = ext{cos}^{-1}(0.4) ext{ or } θ = 60°.$

Therefore, the final answer is:

$θ = 60°.$