A pendulum clock keeps correct time at 0- C- Its mean coefficient of linear expansions is -0- then the loss in seconds per day by the clock if the temperature rises by t 0 C isA- 1-2- t - 864000-1- t-2B- 1-2- t - 86400C- 1-2- t - 86400-1- t-2D- 1-2- t - 86400-1- t-22

The correct option is B Loss in time per second T/T=1/2αθ = 1/2α (t 0) ⇒ loss in time per day t=(1/2α t )t=1/2α t× (24× 60 × 60)=1/2α t × 86400 ...

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Standard XII

Physics

Expression for Torsional Pendulum

A pendulum cl...

Question

A pendulum clock keeps correct time at $0^{o} C$ . Its mean coefficient of linear expansions is $\frac{α}{^{o} C}$ , then the loss in seconds per day by the clock if the temperature rises by $t^{o} C$ is

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Solution

The correct option is B

Loss in time per second $\frac{△ T}{T} = \frac{1}{2} α △ θ = \frac{1}{2} α (t - 0)$
$\Rightarrow$ loss in time per day
$△ t = (\frac{1}{2} α t) t = \frac{1}{2} α t \times (24 \times 60 \times 60) = \frac{1}{2} α t \times 86400$

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Loss in time per second $\frac{△ T}{T} = \frac{1}{2} α △ θ = \frac{1}{2} α (t - 0)$
$\Rightarrow$ loss in time per day
$△ t = (\frac{1}{2} α t) t = \frac{1}{2} α t \times (24 \times 60 \times 60) = \frac{1}{2} α t \times 86400$