A pendulum clock is 5 seconds fast at temperature of 15° C and 10 seconds slow at a temperature of 30° C. At what temperature does it give the correct time? (take time interval =24 hours)

Question

A pendulum clock is 5 seconds fast at temperature of 15° C and 10 seconds slow at a temperature of 30° C. At what temperature does it give the correct time? (take time interval =24 hours) (A) 18° C (B) 20° C (C) 22° C (D) 25° C

Tardigrade Admin · Accepted Answer

Δ t =(1/2) α Δ T × t ∴ 5=(1/2) α( T -15) × 86400 and 10=(1/2) α(30- T ) × 86400

Q. A pendulum clock is $5$ seconds fast at temperature of $1 5^{\circ} C$ and $10$ seconds slow at a temperature of $3 0^{\circ} C$ . At what temperature does it give the correct time? (take time interval $= 24$ hours)

$1 8^{\circ} C$

$2 0^{\circ} C$

$2 2^{\circ} C$

$2 5^{\circ} C$

$Δ t = \frac{1}{2} α Δ T \times t$
$∴ 5 = \frac{1}{2} α (T - 15) \times 86400$
and $10 = \frac{1}{2} α (30 - T) \times 86400$

Q. A pendulum clock is 5 seconds fast at temperature of 15∘C and 10 seconds slow at a temperature of 30∘C. At what temperature does it give the correct time? (take time interval =24 hours)

18∘C

20∘C

22∘C

25∘C