Question

A raft of density 600 g/m\(^3\) and mass 120 kg floats in water. How much weight can be put on the raft to make it just sink?

• A. 120 kg
• B. 200 kg
• C. 40 kg
• D. 80 kg

Hint:

For floating objects, the weight of the displaced water equals the weight of the object and any additional weight to make it sink.

Answer 1

The Correct Option is D

For the raft to just sink, the total weight of the raft and the additional weight must be equal to the buoyant force acting on it. The buoyant force is equal to the weight of the water displaced by the raft. - The volume of the raft is given by: \[ V = \frac{m}{\rho} \] where \( m = 120 \, \text{kg} \) is the mass of the raft, and \( \rho = 600 \, \text{g/m}^3 = 0.6 \, \text{kg/m}^3 \) is the density of the raft. The volume of the raft is: \[ V = \frac{120}{0.6} = 200 \, \text{m}^3 \] The buoyant force is the weight of the water displaced: \[ F_{\text{buoyant}} = \rho_{\text{water}} V g = 1000 \times 200 \times 9.8 = 1.96 \times 10^6 \, \text{N} \] Thus, the additional weight required to make the raft just sink is 80 kg, so the correct answer is (D).