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A steel scale is calibrated to read accurately at 0 deg C. When this scale is used to measure the length of a wooden rod, the readings are 10 cm at 0 deg C and 9.975 cm at 20 deg C. What will the scale read for the same rod at 50 deg C? (Assume the wood expands uniformly.)
- 9.9425 cm
- 9.9375 cm
- 10.0525 cm
- 9.875 cm
Correct answer: 9.9375 cm
Solution
At 0 deg C the true rod length = 10 cm. The scale reads 9.975 cm at 20 deg C, so the true rod length at 20 deg C = 9.975*(1 + alpha_steel*20). Using the expansion of the wooden rod: L0*(1+alpha_wood*20) = 9.975*(1+alpha_steel*20). Solving with alpha_steel = 1.2x10⁻⁵/C gives alpha_wood and then the reading at 50 deg C = 9.9375 cm.
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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