A pendulum clock is 5 seconds fast at a temperature of 150C and 10 seconds slow at a temperature of 300C. The temperature at which it gives the correct time is

ΔTT=12αΔt5T=12αt−1510T=12α30−t⇒510=t−1530−t⇒t=20∘C

A pendulum clock is 5 seconds fast at a temperature of 150C and 10 seconds slow at a temperature of 300C. The temperature at which it gives the correct time is

ΔTT=12αΔt5T=12αt−1510T=12α30−t⇒510=t−1530−t⇒t=20∘C

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A pendulum clock is 5 seconds fast at a temperature of 15⁰C and 10 seconds slow at a temperature of 30⁰C. The temperature at which it gives the correct time is

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18⁰C

$20 ° C$

22⁰C

25⁰C

answer is B.

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Detailed Solution

$\frac{Δ T}{T} = \frac{1}{2} α Δ t$

$\frac{5}{T} = \frac{1}{2} α (t - 15)$

$\frac{10}{T} = \frac{1}{2} α (30 - t)$

$\Rightarrow \frac{5}{10} = \frac{t - 15}{30 - t} \Rightarrow t = 20^{\circ} C$

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A pendulum clock is 5 seconds fast at a temperature of 150C and 10 seconds slow at a temperature of 300C. The temperature at which it gives the correct time is

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A pendulum clock is 5 seconds fast at a temperature of 15⁰C and 10 seconds slow at a temperature of 30⁰C. The temperature at which it gives the correct time is