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A steel tape correctly measures the length of a copper rod as 90.00 cm when both are at 10 deg C (the calibration temperature). When both are heated to 30 deg C, the tape records the length of the rod as 90.0x cm. Find the digit x. (Given: alpha_copper = 1.7 * 10⁻⁵ / deg C, alpha_steel = 1.2 * 10⁻⁵ / deg C)
- 1
- 2
- 3
- 4
Correct answer: 1
Solution
The copper rod expands by alpha_c*L*dT while the steel tape's scale also expands by alphaₛ*L*dT, so the tape reading increases by (alpha_c - alphaₛ)*L*dT = 0.5e-5 * 90 * 20 = 0.009 cm, making the reading 90.009 cm ≈ 90.01 cm, giving x = 1.
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:
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(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.
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(5) The peak wavelength of emitted radiation is suitable for imaging human bones.
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