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 second lost in a day Δ t =(1/2)α Δ θ×86400 The coefficient of linear expansion of metal pendulum α=(2Δ t/Δθ×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 25 $^{\circ}$ 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 second 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 12.5 s a day at 25∘C, the coefficient of linear expansion of metal pendulum is

864001​/∘C

432001​/∘C

144001​/∘C

288001​/∘C