(A) The time period of a simple pendulum is given by $T = 2 \pi \sqrt{\frac{l}{g}}$.Taking the logarithmic derivative, we get $\frac{dT}{T} = \frac{1}

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(A) The time period of a simple pendulum is given by $T = 2 \pi \sqrt{\frac{l}{g}}$.Taking the logarithmic derivative, we get $\frac{dT}{T} = \frac{1}{2} \frac{dl}{l}$.Since the linear expansion is given by $\frac{dl}{l} = \alpha \Delta \theta$, we substitute this into the equation:$\frac{dT}{T} = \frac{1}{2} \alpha \Delta \theta$.Given $\alpha = 9 \times 10^{-7} /{ }^{\circ} C$ and $\Delta \theta = (30 - 20) = 10^{\circ} C$,$\frac{dT}{T} = \frac{1}{2} \times 9 \times 10^{-7} \times 10 = 4.5 \times 10^{-6}$.The loss in time per oscillation is $dT = T \times (4.5 \times 10^{-6})$.Substituting $T = 0.5 \, s$, we get $dT = 0.5 \times 4.5 \times 10^{-6} = 2.25 \times 10^{-6} \, s$.

Class 11 Physics 10-1.Thermometry, Thermal Expansion and Calorimetry Thermal Expansion for Solid

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$A$ clock pendulum made of invar has a period of $0.5 \, s$ at $20^{\circ} C$. If the clock is used in a climate where the temperature averages to $30^{\circ} C$, how much time does the clock lose in each oscillation? (For invar, $\alpha = 9 \times 10^{-7} /{ }^{\circ} C$, $g = \text{constant}$)

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A
$2.25 \times 10^{-6} \, s$
B
$2.5 \times 10^{-7} \, s$
C
$5 \times 10^{-7} \, s$
D
$1.125 \times 10^{-6} \, s$

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$A$ clock pendulum made of invar has a period of $0.5 \, s$ at $20^{\circ} C$. If the clock is used in a climate where the temperature averages to $30^{\circ} C$, how much time does the clock lose in each oscillation? (For invar, $\alpha = 9 \times 10^{-7} /{ }^{\circ} C$, $g = \text{constant}$)

Similar Questions

The length of a metallic rod is $5 \, m$ at $0^{\circ}C$ and becomes $5.01 \, m$ on heating up to $100^{\circ}C$. The coefficient of linear expansion of the metal is:

The volume of a metal sphere increases by $0.30 \%$,when its temperature is raised by $50^{\circ} C$. The coefficient of linear expansion of the metal is

Two rods of same area of cross-section have lengths $L$ and $2 \,L$ and coefficients of linear expansion $2 \alpha$ and $\alpha$ respectively. If they are welded to form a composite rod of length $3 \,L$,then the coefficient of linear expansion of the composite rod is

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