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
~Gracina~, let's knock this out. Step 1: Recall the formula for linear expansion. The change in length ( L) of a material due to a temperature change ( T) is given by: L = L_0 T where L_0 is the original length and is the coefficient of linear expansivity. Step 2: Write down the given information for metals P and Q. • Linear expansivity of P is twice that of Q: _P = 2_Q • Same temperature change: T_P = T_Q = T • Same increase in length: L_P = L_Q • Let the original lengths be L_0P and L_0Q. Step 3: Set up the linear expansion equations for both metals. For metal P: L_P = L_0P _P T For metal Q: L_Q = L_0Q _Q T Step 4: Equate the changes in length and substitute the given conditions. Since L_P = L_Q: L_0P _P T = L_0Q _Q T Substitute _P = 2_Q: L_0P (2_Q) T = L_0Q _Q T Step 5: Solve for the ratio of the original lengths L_0PL_0Q. Divide both sides by _Q T (assuming _Q ≠ 0 and T ≠ 0): 2 L_0P = L_0Q Rearrange to find the ratio L_0PL_0Q: L_0PL_0Q = (1)/(2) The ratio of the original length of P to that of Q is 1:2. The final answer is B. 1:2. Send me the next one 📸