Answer

Verified

348.9k+ views

**Hint:**It is given in the question that the pendulum clock is accurate at $ {0^ \circ }C$ . As the temperature increases the pendulum starts expanding. The thermal coefficient of expansion is used to determine this expansion. TO find the time loss we can use the following formula:

\[\dfrac{{\Delta t}}{t} = \dfrac{1}{2}\alpha \Delta T\]

**Complete answer:**

In this question we are provided with the coefficient of expansion $ \alpha $ .

The rise in temperature is $ {t^ \circ }C$ .

Using the formula,

\[\dfrac{{\Delta t}}{t} = \dfrac{1}{2}\alpha \Delta T\]

\[\dfrac{{\Delta t}}{t}\] Fractional increase in time

$ \alpha $ Coefficient of linear expansion

\[\Delta T\] change in temperature = $ {t^ \circ }C$

Time in day (seconds) $ t = 24 \times 60 \times 60$

Putting all values in the formula e get,

\[

\dfrac{{\Delta t}}{t} = \dfrac{1}{2}\alpha \Delta T \\

\Rightarrow \;\dfrac{{\Delta t}}{{24 \times 60 \times 60}} = \dfrac{1}{2}\alpha (t) \\

\Rightarrow \Delta t = 43200\alpha t \\

\]

So, the time lost per day will be

\[ \Rightarrow \Delta t = 43200\alpha t\] .

**Note:**The loss in time per day of a pendulum may change with the metal used for making the pendulum. As the coefficient of linear expansion is dependent on the properties of metal, time lost will be different for different metal pendulums used. Additionally, the advantage of the pendulum used in clocks is that it is an harmonic oscillator which helps it swing in precise time intervals.

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Why Are Noble Gases NonReactive class 11 chemistry CBSE

Let X and Y be the sets of all positive divisors of class 11 maths CBSE

Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE

Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE

Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE

Trending doubts

Guru Purnima speech in English in 100 words class 7 english CBSE

Which are the Top 10 Largest Countries of the World?

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Select the word that is correctly spelled a Twelveth class 10 english CBSE