A clock pendulum made of invar has a period of 0.5 sec at 20°C. If the clock is used in a climate where average temperature is 30°C, approximately how much fast or slow will the clock run in 106 sec. [αinvar = 1×10

Engineering

Physics

Thermal Expansion

Question

A clock pendulum made of invar has a period of 0.5 sec at 20°C. If the clock is used in a climate where average temperature is 30°C, approximately how much fast or slow will the clock run in 10⁶ sec. [α_invar = 1×10^{– 6}/°C]

5 sec fast

5 sec slow

10 sec slow

10 sec fast

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$T = 2 π \sqrt{\frac{l}{g}} T^{'} = 2 π \sqrt{\frac{l + Δ l}{g}}$

$T^{'} - T = \frac{2 π}{\sqrt{g}} [(l + Δ l)^{1 / 2} - (l)^{1 / 2}] = 2 π \sqrt{\frac{l}{g}} [{(l + \frac{Δ l}{l})}^{1 / 2} - 1]$

$= 2 π \sqrt{\frac{l}{g}} [\frac{1}{2} \frac{Δ l}{l}] = \frac{2 π}{2} \sqrt{\frac{l}{g}} αΔt$

$= \frac{0.5}{2} \times 10^{- 6} \times 10$

$no. of ossi = \frac{10^{- 6}}{0.5} \times \frac{0.5}{2} \times 10^{- 6} \times 10 = 5 \sec$ .