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
To solve this problem, we will first find the mass of the paraffin, then use the relative density of paraffin to find the mass of an equal volume of water, and finally calculate the total mass of the bottle when filled with water. Step 1: Calculate the mass of the paraffin. The mass of the empty bottle is 30 g. The mass of the bottle filled with paraffin is 70 g. The mass of the paraffin (m_paraffin) is the difference between these two masses: m_paraffin = m_bottle+paraffin - m_empty m_paraffin = 70 g - 30 g m_paraffin = 40 g Step 2: Use the relative density of paraffin to find the mass of an equal volume of water. Relative density (RD) is defined as the ratio of the density of a substance to the density of water. For equal volumes, it is also the ratio of the mass of the substance to the mass of water. RD_paraffin = m_paraffinm_water (same volume) We are given RD_paraffin = 0.8 and we found m_paraffin = 40 g. We need to find m_water (same volume). 0.8 = 40 gm_water (same volume) Rearrange the formula to solve for m_water (same volume): m_water (same volume) = 40 g0.8 m_water (same volume) = 50 g Step 3: Calculate the mass of the bottle when filled with water. The mass of the bottle filled with water (m_bottle+water) is the sum of the mass of the empty bottle and the mass of the water that fills it: m_bottle+water = m_empty + m_water (same volume) m_bottle+water = 30 g + 50 g m_bottle+water = 80 g The final answer is 80 g.