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.
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12. (a) Step 1: Select two metal tubes P and Q of identical diameter and same initial length L. Tube P has known coefficient of linear expansion _P (e.g., steel tube, _P = 11 × 10^-6 \, K^-1). Tube Q has unknown coefficient _Q. Step 2: Fix one end of both tubes rigidly to a common support. Attach the free ends to a rigid crossbar or use a micrometer screw gauge to measure relative displacement . Step 3: Heat both tubes uniformly (e.g., with steam jacket), raising temperature by T (measured by thermometer in ^ or K). The change in length for tube P: L_P = L _P T. The change in length for tube Q: L_Q = L _Q T. Relative displacement: = L_Q - L_P = L (_Q - _P) T. Step 4: Solve for _Q: _Q = _P + ()/(L T). Units: in m, L in m, T in K, in K^-1. This uses the principle of linear thermal expansion L = L T. 12. (b) For a uniform rectangular lamina ABCD, the centre of mass (COM) is at the geometric centre. Method using straight edge: Step 1: Place lamina on white paper. Step 2: Use straight edge to draw diagonal from corner A to C. Step 3: Use straight edge to draw diagonal from corner B to D. Step 4: Mark intersection point O — this is the COM. Labelled diagram description: Rectangle ABCD: A top-left, B top-right, C bottom-right, D bottom-left. Diagonal AC and BD cross at O (COM). To verify with plumbline apparatus (using straight edge to mark lines): Step 1: Punch three holes near edges (e.g., close to A, B, midway on CD). Step 2: Suspend lamina from hole 1 via pin on stand; hang plumb bob, mark plumb line on paper using straight edge. Step 3: Repeat for holes 2 and 3. Step 4: Lines intersect at COM (same as O). COM at intersection of diagonals or plumb lines.