This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
Here's how to calculate the density of the stone: i) Density in gcm^-3 Step 1: Calculate the volume of the stone. The water level rises from 9 cm (from the previous problem) to 12 cm when the stone is lowered. The volume of the stone is equal to the volume of the displaced water. Change in water height ( h) = Final height - Initial height h = 12 cm - 9 cm = 3 cm The base dimensions of the tank are 17 cm by 8 cm. Volume of the stone (V_stone) = Length × Width × h V_stone = 17 cm × 8 cm × 3 cm V_stone = 408 cm^3 Step 2: Calculate the density of the stone in g/cm^3. Mass of the stone (m) = 2400 g Density () = (m)/(V_stone) = 2400 g408 cm^3 ≈ 5.882 g/cm^3 The density of the stone in gcm^-3 is 5.882 g/cm^3. ii) Density in kgm^-3 Step 1: Convert the mass from grams to kilograms. m = 2400 g = 2400 × 1 kg1000 g = 2.4 kg Step 2: Convert the volume from cubic centimeters to cubic meters. V_stone = 408 cm^3 Since 1 m = 100 cm, then 1 m^3 = (100 cm)^3 = 1,000,000 cm^3. V_stone = 408 cm^3 × 1 m^31,000,000 cm^3 = 0.000408 m^3 Step 3: Calculate the density of the stone in kg/m^3. = (m)/(V_stone) = 2.4 kg0.000408 m^3 ≈ 5882.353 kg/m^3 Alternatively, convert directly from g/cm^3: 1 g/cm^3 = 1000 kg/m^3 = 5.882 g/cm^3 × 1000 = 5882 kg/m^3 The density of the stone in kgm^-3 is 5882.353 kg/m^3. Last free one today — make it count tomorrow, or type /upgrade for unlimited.