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MHT CET202526 Apr 2025Morning ShiftPhysicsThermal Properties of MatterActual

The difference in length between two rods A and B is 60 cm at all temperatures. If _A=18 10⁻⁶ / ^ C and _B=27 10⁻⁶ / ^ C , then the length of rod A and rod B at 0^ C is respectively

Options

  1. A_ A =120 ~cm , _ B =60 ~cm .
  2. B_ A =180 ~cm , _ B =120 ~cm .
  3. C_ A =240 ~cm , _ B =180 ~cm .
  4. D_ A =270 ~cm , _ B =210 ~cm .

Correct answer

B. _ A =180 ~cm , _ B =120 ~cm .

Step-by-step solution

The constant length difference of 60 cm at all temperatures implies the thermal expansion terms must cancel. At T = 0^ C , L_ A0 - L_ B0 = 60 . For arbitrary temperature T , the difference is L_ A0 (1 + _A T) - L_ B0 (1 + _B T) = 60 . Substituting the known constant difference yields (L_ A0 _A - L_ B0 _B)T = 0 for all T , requiring L_ A0 _A = L_ B0 _B . Given _A = 18 10⁻⁶/^ C and _B = 27 10⁻⁶/^ C , we obtain L_ A0 /L_ B0 = _B/ _A = 3/2 . Substituting L_ A0 = (3/2)L_ B0 into the length difference equation gives (1/2

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