A pendulum clock keeps correct time at 0° C. Its mean coefficient of linear expansions is α/ ° C , then the loss in time (in sec) per day by the clock if the temperature rises by t ° C is

Question

A pendulum clock keeps correct time at 0° C. Its mean coefficient of linear expansions is α/ ° C , then the loss in time (in sec) per day by the clock if the temperature rises by t ° C is (A) (α t/2) (B) (1/2) α t (C) 43200 α t (D)  86400 α t

Tardigrade Admin · Accepted Answer

Loss in time per day, (Δ T / T ) =(1/2) α Δ θ × 24 × 60 × 60 ∴ (Δ T / T )=(1/2) α Δ θ × 86400 =(1/2) × α t × 86400 (Δ T / T )= α t 43200

Q. A pendulum clock keeps correct time at $0^{\circ} C$ . Its mean coefficient of linear expansions is $α^{/ \circ} C,$ then the loss in time (in sec) per day by the clock if the temperature rises by $t^{\circ} C$ is

$\frac{α t}{2}$

$\frac{1}{2} α t$

$43200 α t$

$86400 α t$

Loss in time per day, $\frac{Δ T}{T}$
$= \frac{1}{2} α Δ θ \times 24 \times 60 \times 60$
$∴ \frac{Δ T}{T} = \frac{1}{2} α Δ θ \times 86400$
$= \frac{1}{2} \times α t \times 86400$
$\frac{Δ T}{T} = α t 43200$

Q. A pendulum clock keeps correct time at 0∘C. Its mean coefficient of linear expansions is α/∘C, then the loss in time (in sec) per day by the clock if the temperature rises by t∘C is

2αt​

21​αt

43200αt

86400αt