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Three rods of equal length L are joined to form an equilateral triangle PQR. O is the midpoint of PQ. For a small change in temperature, the distance OR remains constant. The coefficient of linear expansion for rods PR and RQ is alpha₂, and for rod PQ it is alpha₁. Find the relationship between alpha₁ and alpha₂.
- alpha₂ = 3 * alpha₁
- alpha₂ = 4 * alpha₁
- alpha₁ = 3 * alpha₂
- alpha₁ = 4 * alpha₂
Correct answer: alpha₁ = 4 * alpha₂
Solution
In equilateral triangle PQR with side L, O is midpoint of PQ. OR = height of triangle = L*sqrt(3)/2. RQ = L, OQ = L/2. When temperature changes: d(RQ) = alpha₂*L*dT, d(OQ) = (alpha₁/2)*L*dT (half of PQ expansion since O is midpoint of PQ). Setting d(OR) = 0 and using differentiation of RQ² = OR² + OQ².
Related JEE Advanced Physics questions
- Match the temperature of a blackbody listed in Group-I to the corresponding statement in Group-II, and select the correct answer.
[Given: Wien’s constant = 2.9 × 10⁻³ m-K and hc/e = 1.24 × 10⁻⁶ V-m]
Group-I:
(P) 2000 K
(Q) 3000 K
(R) 5000 K
(S) 10000 K
Group-II:
(1) The peak wavelength of emitted radiation can cause photoelectron ejection from a metal with a work function of 4 eV.
(2) The peak wavelength of emitted radiation falls within the visible spectrum.
(3) The peak wavelength of emitted radiation produces the broadest central diffraction maximum in a single-slit setup.
(4) The energy radiated per unit area is one-sixteenth of that emitted by a blackbody at 6000 K.
(5) The peak wavelength of emitted radiation is suitable for imaging human bones.
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- A steel rail track of length 1 km was laid at an ambient temperature of 20 deg C with no gaps for thermal expansion. When the temperature rose to 25 deg C, the track buckled and formed an isosceles triangle shape. Given the coefficient of linear expansion of steel is 14 * 10⁻⁶ per K, find the height of the buckle in metres (to the nearest integer).
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- A continuous-flow calorimeter is used in two separate experiments to find the specific heat of a liquid. In the first trial, supplying 60 W raises the liquid temperature by 10 K. In the second trial, the power is doubled to 120 W, but the same 10 K rise is maintained by tripling the flow rate. Assuming heat loss to surroundings is the same in both trials, what is the power lost to the surroundings?
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