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Q.

Two rods of same mass and same length lo but having different coefficient of expansions α and 3α are joined at P (see figure). System is placed on frictionless surface. Iftemperature of whole system is changed by ∆T, the displacement of junction point is

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a

l∘αΔT

b

2l∘αΔT

c

l0αΔT2

d

34l0αΔT

answer is C.

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Detailed Solution

Net force on the system is zero hence displacement of the centre of mass of the system will be zero.Let x be the shift in P, thenml∘2(1+αΔT)+x=ml∘2(1+3αΔT)−x⇒x=l0αΔT2∴  (3)
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Two rods of same mass and same length lo but having different coefficient of expansions α and 3α are joined at P (see figure). System is placed on frictionless surface. Iftemperature of whole system is changed by ∆T, the displacement of junction point is