Gce Model Questions Vol1 2025 Physics Question 40

A 0.75 kg block of an unknown metal is heated to (200^{\circ}\text{C}\) and then placed into a well‑insulated calorimeter containing (3.0\;\text{kg}\) of water initially at (25^{\circ}\text{C}\). After the system reaches thermal equilibrium the temperature of the water and the metal is (35^{\circ}\text{C}\). (The specific heat capacity of water is (4186\;\text{J\,kg}^{-1}\text{K}^{-1}\).)\n\n(a) Determine the specific heat capacity of the metal in \(\text{J\,kg}^{-1}\text{K}^{-1}\).\n\n(b) The metal has a density of \(8900\;\text{kg\,m}^{-3}\). If a cylindrical rod of this metal has a radius of \(1.5\;\text{cm}\), find the length of the rod that would have the same mass as the block. Give your answer for the length to two significant figures.