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A pendulum clock loses 12 s a day if the temperature is 40 °C and gains 4 s a day if the temperature is 20 °C. The temperature at which the clock will show correct time, and the coefficient of linear expansion α of the metal of the pendulum shaft are respectively

Asked in JEE Main 2016 · Pendulum clock with temperature

• (1) 25 °C; α=1.85×10⁻⁵ °C⁻¹
• (2) 60 °C; α=1.85×10⁻⁴ °C⁻¹
• (3) 30 °C; α=1.85×10⁻³ °C⁻¹
• (4) 55 °C; α=1.85×10⁻² °C⁻¹

Step-by-step solution

Why the other options are wrong

• (2) comes from puts the correct-time temperature outside the bracket 20 °C to 40 °C. A clock that runs fast at 20 °C and slow at 40 °C must keep time somewhere between the two, since the daily error 1/2αΔ T×86400 changes sign only once.
• (3) comes from takes the plain midpoint of 20 and 40. That would be right only if the two errors were equal; here the loss is 12 s and the gain only 4 s, so T₀ must sit three times as far from 40 °C as from 20 °C, giving 25 °C.
• (4) comes from no consistent slip lands here; it is a filler outside the bracket. The nearest wrong route worth checking, inverting the ratio of the errors so that (40-T₀)/(T₀-20)=1/3, gives 35 °C, not 55.

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