A second's pendulum clock having steel wire is calibrated at 20^∘ C. When temperature is increas

step 1 Hello students in this question we have a second spandulum clock having steel wire is calibrated

A second's pendulum clock having steel wire is calibrated at...

A second's pendulum clock having steel wire is calibrated at $20^{\circ} \mathrm{C}$. When temperature is increased to $30^{\circ} \mathrm{C}$, then how much time does the clock lose or gain in one week ? $\left[\alpha_{\text {steel }}=1.2 \times 10^{-5}\left({ }^{\circ} \mathrm{C}\right)^{-1}\right]$ (a) $0.3628 \mathrm{~s}$ (b) $3.626 \mathrm{~s}$ (c) $362.8 \mathrm{~s}$ (d) $36.28 \mathrm{~s}$

A second's pendulum clock having steel wire is calibrated at $20^{\circ} \mathrm{C}$. When temperature is increased to $30^{\circ} \mathrm{C}$, then how much time does the clock lose or gain in one week ? $\left[\alpha_{\text {steel }}=1.2 \times 10^{-5}\left({ }^{\circ} \mathrm{C}\right)^{-1}\right]$
(a) $0.3628 \mathrm{~s}$
(b) $3.626 \mathrm{~s}$
(c) $362.8 \mathrm{~s}$
(d) $36.28 \mathrm{~s}$

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Accumulation of Small Errors Over Time

Even a minute change per oscillation can accumulate to a significant error when repeated over many cycles. In timekeeping devices such as clocks, a small relative change in the period due to thermal expansion leads to a measurable loss or gain in time over longer durations, such as a week. This concept emphasizes how systematic errors from physical changes can accumulate to affect overall performance.

Thermal Expansion

Thermal expansion is the tendency of matter—particularly solids—to change in size or volume in response to a change in temperature. In the context of the pendulum clock, the steel wire expands when the temperature rises. This expansion increases the effective length of the pendulum, which in turn increases its period and causes a deviation in timekeeping.

Simple Pendulum Dynamics

This concept refers to the formula for the period of a simple pendulum, which is given by T = 2??(L/g). It shows that the period (and therefore the ticking rate of a pendulum clock) depends on the length of the pendulum. An increase in length, even if slight, leads to an increase in the period, thereby affecting the clock’s timekeeping accuracy.

Transcript

Please give Ace some feedback