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 find the temperature at which the steel plug will fit into the hole, we use the formula for linear thermal expansion: L = L_0 (1 + T) where: L is the final length (diameter) L_0 is the initial length (diameter) is the coefficient of linear expansion T is the change in temperature ( T = T - T_0) Step 1: Identify the given values. Initial diameter, L_0 = 5 \, cm Initial temperature, T_0 = 30^ C Final diameter, L = 4.997 \, cm Coefficient of linear expansion, = 11 × 10^-6 \, C^-1 Step 2: Calculate the change in length ( L). L = L - L_0 = 4.997 \, cm - 5 \, cm = -0.003 \, cm Step 3: Rearrange the thermal expansion formula to solve for T. L = L_0 (1 + T) (L)/(L_0) = 1 + T (L)/(L_0) - 1 = T (L - L_0)/(L_0) = T T = (L - L_0)/(L_0 ) Step 4: Substitute the values into the formula to find T. T = -0.003 \, cm(5 \, cm) × (11 × 10^-6 \, C^-1) T = (-0.003)/(55 × 10^-6) \, C T = (-0.003)/(0.000055) \, C T ≈ -54.545 \, C Step 5: Calculate the final temperature (T). T = T - T_0 T = T_0 + T T = 30^ C + (-54.545^ C) T = 30^ C - 54.545^ C T ≈ -24.545^ C Rounding to one decimal place, T ≈ -24.5^ C. Step 6: Compare with the given options. The calculated temperature matches option B. The final answer is B. Last free one today — make it count tomorrow, or type /upgrade for unlimited.