A pendulum clock gives correct time at the equator. Will it gain time or lose time as it is taken to the poles?
Answers
Answer ⇒ Pendulum clock will loses the time on the Poles.
Explanation ⇒ As we know the formula,
T = 2π √(l/g), where, T is the Time period of the pendulum, and l is the length of the pendulum, and g is the acceleration due to the gravity.
From, this expression we can say that Time period is inversely proportional to the square root of the acceleration due to the gravity, keeping the length constant and avoiding the change in length due to the thermal expansion.
Now, We also know,
g' = g - rω²cos²θ
At Equator, θ = 0,
thus, g' = g - rω² which is minimum.
This means, Time period will be maximum as they are inversely related.
Also, At Poles, θ = 0
thus, g' = g, which is maximum.
This means, Time period will be minimum, as they are inversely related.
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Hence, its time losses when it goes to the Poles.
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Hope it helps.