9. (a) A right circular solid cylinder floats at rest in water with its axis vertical - Leaving Cert Applied Maths - Question 9 - 2009

For the sphere held in equilibrium, the buoyant force, tension in the string (T), and the weight of the sphere (W) are related by:

$B + T = W$

The weight of the sphere is calculated as:

$W = ext{Density}_{sphere} imes V imes g$

Where the volume of the sphere is:

V = rac{4}{3} imes rac{22}{7} imes (0.07^3)

Calculating W gives:

$W = 3 imes 1000 imes 0.000143 imes 9.81$

After simplifying, we find that:

$W ext{ is approximately } 4.13 ext{ N}$

Now we can find T by substituting into the previous equation:

$T = W - B$

Since the relative density of the liquid is given, we find that the buoyant force can also be calculated using the formula for buoyant force.

Finally calculating T gives:

$T ext{ (tension in string) is approximately } 31.62 ext{ N}$.