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10.1, thermonetry,thermal expansion and calorimetry — Physics STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 SciencePhysics10.1, thermonetry,thermal expansion and calorimetry1 Mark
MCQ
A pendulum clock (fitted with a small heavy bob that is connected with a metal rod) is $5\, seconds$ fast each day at a temperature of $15\,^oC$ and $10\,seconds$ slow at a temperature of $30\,^oC$. The temperature at which it is designed to give correct time, is ........ $^oC$
  • A
    $18$
  • ✓
    $20$
  • C
    $24$
  • D
    $25$
✓

Answer

Correct option: B.
$20$
b
$\Delta \mathrm{t}=\frac{1}{2} \alpha \Delta \theta \mathrm{t}$

$5=\frac{1}{2} \alpha[\theta-15] \times 1 \mathrm{Day}$           $...(1)$

$10=\frac{1}{2} \alpha[30-\theta] \times 1 \mathrm{Day}$       $...(2)$

$\mathrm{Eq}-(1) \div(2)$

$\frac{1}{2}=\frac{\theta-15}{30-\theta} \Rightarrow 30-\theta=2 \theta-30 \Rightarrow \theta=20^{\circ} \mathrm{C}$

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