9. (a) A solid rectangular block is used as a floating platform - Leaving Cert Applied Maths - Question 9 - 2019

The mass of the platform can be calculated using the relation between weight and mass:

1. Rearranging the formula for weight: $W = m imes g$ Therefore, $m = \frac{W}{g}$

2. Substituting the values: $m = \frac{480000}{10} = 48000 \text{ kg}$

3. Convert mass into tonnes:

   • 1 tonne = 1000 kg, so: $m = \frac{48000}{1000} = 48 \text{ tonnes}$

The tension in the string can be determined considering the forces acting on the sphere.

1. The weight of the sphere is given by: $W_{sphere} = m_{sphere} imes g$ Where the mass can be derived from the relative density:

   • The volume of the sphere: $V_{sphere} = \frac{4}{3} \pi r^3 = \frac{4}{3} \pi (0.12)^3 \text{ m}^3$
   • Given the relative density (0.7), the mass of the sphere will be: $m_{sphere} = 0.7 \times V_{sphere} \times (1.5 \times 1000)$
   • Thus, substituting into the weight formula: $W_{sphere} = 0.7 \times \frac{4}{3} \pi (0.12)^3 \times (1500 \text{ kg/m}^3) \times 9.81$

2. Then set up the vertical force balance: $T + W_{sphere} = B$ Where B is the buoyancy force: $B = V_{sphere} \times \rho_{liquid} \times g$ Substituting known values will yield the final tension in the string.