A clock with a metal pendulum beating seconds keeps correct time at 0° C. If it loses 12.5 s a day at 25° C, the coefficient of linear expansion of metal pendulum is

Question

A clock with a metal pendulum beating seconds keeps correct time at 0° C. If it loses 12.5 s a day at 25° C, the coefficient of linear expansion of metal pendulum is (A) (1/86400) / ° C (B) (1/43200) / ° C (C) (1/14400) / ° C (D) (1/28800) / ° C

Tardigrade Admin · Accepted Answer

Number of seconds lost in a day Δ t=(1/2) α Δ θ × 86400 The coefficient of linear expansion of metal pendulum α=(2 Δ t/Δ θ × 86400)=(2 × 12.5/25 × 86400) α=(1/86400) / ° C

Q. A clock with a metal pendulum beating seconds keeps correct time at $0^{\circ} C$ . If it loses $12.5 s$ a day at $2 5^{\circ} C$ , the coefficient of linear expansion of metal pendulum is

$\frac{1}{86400} /^{\circ} C$

$\frac{1}{43200} /^{\circ} C$

$\frac{1}{14400} /^{\circ} C$

$\frac{1}{28800} /^{\circ} C$

Number of seconds lost in a day
$Δ t = \frac{1}{2} α Δ θ \times 86400$
The coefficient of linear expansion of metal pendulum
$α = \frac{2Δ t}{Δ θ \times 86400} = \frac{2 \times 12.5}{25 \times 86400}$
$α = \frac{1}{86400} /^{\circ} C$

Q. A clock with a metal pendulum beating seconds keeps correct time at 0∘C. If it loses 12.5s a day at 25∘C, the coefficient of linear expansion of metal pendulum is

864001​/∘C

432001​/∘C

144001​/∘C

288001​/∘C