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A poorly designed electrostatic device contains two metal bolts — one steel and one copper — positioned facing each other with an initial gap of 21.55 micrometers at 27 degrees C. The steel bolt has length 0.1 m and the copper bolt has length 0.3 m. Given the linear expansion coefficients alpha_steel = 3.55 * 10⁻⁵ per K and alpha_copper = 6 * 10⁻⁵ per K, which of the following statements is/are correct?
- The temperature at which the gap between the bolts closes is 28 degrees C
- The temperature at which the gap between the bolts closes is 27.5 degrees C
- The change in length of the steel bolt when the gap closes is 3.55 micrometers
- The change in length of the copper bolt when the gap closes is 13.55 micrometers
Correct answer: The temperature at which the gap between the bolts closes is 28 degrees C
Solution
The gap closes when the sum of expansions equals the gap: Lₛ*alphaₛ*DT + L_c*alpha_c*DT = gap. DT*(0.1*3.55e-5 + 0.3*6e-5) = 21.55e-6. DT*(3.55e-6 + 18e-6) = 21.55e-6. DT*21.55e-6 = 21.55e-6 => DT = 1 K. Final temperature = 27 + 1 = 28 degrees C (option A correct). Delta_L_steel = 0.1*3.55e-5*1 = 3.55e-6 m = 3.55 micrometers (option C correct). Delta_L_copper = 0.3*6e-5*1 = 18e-6 m = 18 micrometers, not 13.55 (option D wrong).
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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