Advertisements
Advertisements
प्रश्न
As the temperature is increased, the time period of a pendulum ______.
पर्याय
increases as its effective length increases even though its centre of mass still remains at the centre of the bob.
decreases as its effective length increases even though its centre of mass still remains at the centre of the bob.
increases as its effective length increases due to shifting of centre of mass below the centre of the bob.
decreases as its effective length remains same but the centre of mass shifts above the centre of the bob.
Advertisements
उत्तर
As the temperature is increased, the time period of a pendulum increases as its effective length increases even though its centre of mass still remains at the centre of the bob.
Explanation:
A pendulum clock keeps proper time at temperature θ0. If the temperature is increased to θ (> θ0), then due to linear expansion, the length of pendulum increases and hence its time period will increase
Let T = `2πsqrt(L_0/g)` at temperature θ0
And T' = `2πsqrt(L/g)` at temperature θ.
`T^'/T = sqrt(L^'/L)`
= `sqrt((L[1 + αΔθ])/L`
= `1 + 1/2 αΔθ`
Therefore change (loss or gain) in time per unit time lapsed is `(T^' - T)/T = 1/2 αΔθ`
Fractional change in time period `(ΔT)/T = 1/2 αΔθ`
So, as the temperature increases, the length of pendulum increases and hence time period of the pendulum increases. Due to an increment in its time period, a pendulum clock becomes slow in summer and will lose time.
APPEARS IN
संबंधित प्रश्न
A hole is drilled in a copper sheet. The diameter of the hole is 4.24 cm at 27.0 °C. What is the change in the diameter of the hole when the sheet is heated to 227 °C? Coefficient of linear expansion of copper = 1.70 × 10–5 K–1.
A brass rod of length 50 cm and diameter 3.0 mm is joined to a steel rod of the same length and diameter. What is the change in length of the combined rod at 250 °C, if the original lengths are at 40.0 °C? Is there a ‘thermal stress’ developed at the junction? The ends of the rod are free to expand (Co-efficient of linear expansion of brass = 2.0 × 10–5 K–1, steel = 1.2 × 10–5 K–1).
A 10 kW drilling machine is used to drill a bore in a small aluminium block of mass 8.0 kg. How much is the rise in temperature of the block in 2.5 minutes, assuming 50% of power is used up in heating the machine itself or lost to the surroundings Specific heat of aluminium = 0.91 J g–1 K–1
If two bodies are in thermal equilibrium in one frame, will they be in thermal equilibrium in all frames?
If an automobile engine is overheated, it is cooled by pouring water on it. It is advised that the water should be poured slowly with the engine running. Explain the reason.
For a constant-volume gas thermometer, one should fill the gas at
A gas thermometer measures the temperature from the variation of pressure of a sample of gas. If the pressure measured at the melting point of lead is 2.20 times the pressure measured at the triple point of water, find the melting point of lead.
The density of water at 0°C is 0.998 g cm–3 and at 4°C is 1.000 g cm–1. Calculate the average coefficient of volume expansion of water in the temperature range of 0 to 4°C.
A steel rod is clamped at its two ends and rests on a fixed horizontal base. The rod is unstrained at 20°C.
Find the longitudinal strain developed in the rod if the temperature rises to 50°C. Coefficient of linear expansion of steel = 1.2 × 10–5 °C–1.
Answer the following question.
What is thermal stress?
Solve the following problem.
In olden days, while laying the rails for trains, small gaps used to be left between the rail sections to allow for thermal expansion. Suppose the rails are laid at room temperature 27 °C. If maximum temperature in the region is 45 °C and the length of each rail section is 10 m, what should be the gap left given that α = 1.2 × 10–5K–1 for the material of the rail section?
A uniform metallic rod rotates about its perpendicular bisector with constant angular speed. If it is heated uniformly to raise its temperature slightly ______.
A student records the initial length l, change in temperature ∆T and change in length ∆l of a rod as follows:
| S.No. | l(m) | ∆T (C) | ∆l (m) |
| 1. | 2 | 10 | `4 xx 10^-4` |
| 2. | 1 | 10 | `4 xx 10^-4` |
| 3. | 2 | 20 | `2 xx 10^-4` |
| 4. | 3 | 10 | `6 xx 10^-4` |
If the first observation is correct, what can you say about observations 2, 3 and 4.
Calculate the stress developed inside a tooth cavity filled with copper when hot tea at temperature of 57°C is drunk. You can take body (tooth) temperature to be 37°C and α = 1.7 × 10–5/°C, bulk modulus for copper = 140 × 109 N/m2.
At what temperature a gold ring of diameter 6.230 cm be heated so that it can be fitted on a wooden bangle of diameter 6.241 cm? Both diameters have been measured at room temperature (27°C). (Given: coefficient of linear thermal expansion of gold αL = 1.4 × 10-5 K-1).
Each side of a box made of metal sheet in cubic shape is 'a' at room temperature 'T', the coefficient of linear expansion of the metal sheet is 'α'. The metal sheet is heated uniformly, by a small temperature ΔT, so that its new temeprature is T + ΔT. Calculate the increase in the volume of the metal box.
If the length of a cylinder on heating increases by 2%, the area of its base will increase by ______.
An anisotropic material has coefficient of linear thermal expansion α1, α2 and α3 along x, y and z-axis respectively. Coefficient of cubical expansion of its material will be equal to ______.
Which of the following correctly lists the three types of thermal expansion?
