Advertisements
Advertisements
Question
A torsional pendulum consists of a solid disc connected to a thin wire (α = 2.4 × 10–5°C–1) at its centre. Find the percentage change in the time period between peak winter (5°C) and peak summer (45°C).
Advertisements
Solution
Given:
Coefficient of linear expansion of the wire, α = 2.4 × 10–5 °C–1
Let I0 be the moment of inertia of the torsional pendulum at 0 °C.
If K is the torsional constant of the wire, then time period of torsional pendulum (T):
`T = 2pi sqrt(1/K)`...(1)
Here, I = moment of inertia after change in temperature
When the temperature is changed by Δθ, moment of inertia (I),
l = l0(1+2αΔθ)
On substituting the value of I in equation(1), we get:
`T = 2 pi sqrt( I_0(1+2αΔθ))/sqrt K`
In winter , Δθ = 5 °C
∴ Time period , (T1)
= `2pi sqrt( I_0(1+2αΔθ))/sqrt K`
In summer , Δθ = 45 °C
Time period (T2)
`=2pi sqrt( I_0(1+2αΔθ))/sqrt K`
So,
`T_2/T_1 = sqrt(1+90α)/sqrt(1+10α)`
=`sqrt(1+90 xx 2.4 xx 10^-5)/sqrt(1+10 xx 2.4 xx 10^-5)`
`=> T_2/T_1 = sqrt(1.00216)/sqrt(1.00024)`
% change = `(T_2/T_1 -1) xx 100`
= 0.0959 %
⇒ % change in time period ≈ 9.6 × 10-2 %
Therefore, the percentage change in time period of a torsional pendulum between peak winters and peak summers is 9.6 × 10–2 % .
APPEARS IN
RELATED QUESTIONS
The triple points of neon and carbon dioxide are 24.57 K and 216.55 K respectively. Express these temperatures on the Celsius and Fahrenheit scales.
Two absolute scales A and B have triple points of water defined to be 200 A and 350 B. What is the relation between TA and TB?
The electrical resistance in ohms of a certain thermometer varies with temperature according to the approximate law:
R = Ro [1 + α (T – To)]
The resistance is 101.6 Ω at the triple-point of water 273.16 K, and 165.5 Ω at the normal melting point of lead (600.5 K). What is the temperature when the resistance is 123.4 Ω?
Answer the following:
The triple-point of water is a standard fixed point in modern thermometry. Why? What is wrong in taking the melting point of ice and the boiling point of water as standard fixed points (as was originally done in the Celsius scale)?
Two ideal gas thermometers Aand Buse oxygen and hydrogen respectively. The following observations are made:
| Temperature | Pressure thermometer A | Pressure thermometer B |
| Triple-point of water | 1.250 × 105 Pa | 0.200 × 105 Pa |
| Normal melting point of sulphur | 1.797 × 105 Pa | 0.287 × 105 Pa |
(a) What is the absolute temperature of the normal melting point of sulphur as read by thermometers Aand B?
(b) What do you think is the reason behind the slight difference in answers of thermometers Aand B? (The thermometers are not faulty). What further procedure is needed in the experiment to reduce the discrepancy between the two readings?
In defining the ideal gas temperature scale, it is assumed that the pressure of the gas at constant volume is proportional to the temperature T. How can we verify whether this is true or not? Do we have to apply the kinetic theory of gases? Do we have to depend on experimental result that the pressure is proportional to temperature?
Consider the following statements.
(A) The coefficient of linear expansion has dimension K–1.
(B) The coefficient of volume expansion has dimension K–1.
If the temperature of a uniform rod is slightly increased by ∆t, its moment of inertia I about a perpendicular bisector increases by
The pressure of the gas in a constant volume gas thermometer is 70 kPa at the ice point. Find the pressure at the steam point.
An aluminium vessel of mass 0.5 kg contains 0.2 kg of water at 20°C. A block of iron of mass 0.2 kg at 100°C is gently put into the water. Find the equilibrium temperature of the mixture. Specific heat capacities of aluminium, iron and water are 910 J kg−1 K−1, 470 J kg−1 K−1 and 4200 J kg−1 K−1 respectively.
A piece of iron of mass 100 g is kept inside a furnace for a long time and then put in a calorimeter of water equivalent 10 g containing 240 g of water at 20°C. The mixture attains and equilibrium temperature of 60°C. Find the temperature of the furnace. Specific heat capacity of iron = 470 J kg−1 °C−1.
The temperatures of equal masses of three different liquids A, B and C are 12°C, 19°C and 28°C respectively. The temperature when A and B are mixed is 16°C, and when B and C are mixed, it is 23°C. What will be the temperature when A and C are mixed?
Two metre scales, one of steel and the other of aluminium, agree at 20°C. Calculate the ratio aluminium-centimetre/steel-centimetre at (a) 0°C, (b) 40°C and (c) 100°C. α for steel = 1.1 × 10–5 °C–1 and for aluminium = 2.3 × 10–5°C–1.
A metre scale is made up of steel and measures correct length at 16°C. What will be the percentage error if this scale is used (a) on a summer day when the temperature is 46°C and (b) on a winter day when the temperature is 6°C? Coefficient of linear expansion of steel = 11 × 10–6 °C–1.
A metre scale made of steel reads accurately at 20°C. In a sensitive experiment, distances accurate up to 0.055 mm in 1 m are required. Find the range of temperature in which the experiment can be performed with this metre scale. Coefficient of linear expansion of steel = 11 × 10–6 °C–1.
A glass vessel measures exactly 10 cm × 10 cm × 10 cm at 0°C. It is filled completely with mercury at this temperature. When the temperature is raised to 10°C, 1.6 cm3 of mercury overflows. Calculate the coefficient of volume expansion of mercury. Coefficient of linear expansion of glass = 6.5 × 10–1 °C–1.
A steel rod is rigidly clamped at its two ends. The rod is under zero tension at 20°C. If the temperature rises to 100°C, what force will the rod exert on one of the clamps? Area of cross-section of the rod is 2.00 mm2. Coefficient of linear expansion of steel is 12.0 × 10–6 °C–1 and Young's modulus of steel is 2.00 × 1011 Nm–2.
A metal block of density 600 kg m−3 and mass 1.2 kg is suspended through a spring of spring constant 200 N m−1. The spring-block system is dipped in water kept in a vessel. The water has a mass of 260 g and the bloc is at a height 40 cm above the bottom of the vessel. If the support of the spring is broken, what will be the rise in the temperature of the water. Specific heat capacity of the block is 250 J kg−3 K−1 and that of water is 4200 J kg−1 K−1. Heat capacities of the vessel and the spring are negligible.
Answer the following question.
How a thermometer is calibrated?
At what temperature, the reading of a fahrenheit thermometer will be three times that of celsius thermometer?
If the temperature on the Fahrenheit scale is 140 °F, then the same temperature on the Kelvin scale will be:
Calculate the temperature which has same numeral value on celsius and Fahrenheit scale.
The Zeroth Law of Thermodynamics is the basis for which of the following?
At what temperature do the Celsius and Fahrenheit scales show the same reading?
Convert 37 °C (normal body temperature) to Kelvin.
Which of the following correctly describes an adiabatic wall?
A platinum wire is used as the thermometric substance in a resistance thermometer. What is the thermometric property being utilised here?
A mercury thermometer has a column length of 20 mm at the ice point and 170 mm at the steam point. If the column length is 65 mm, what is the temperature?
Which of the following is NOT a characteristic of a good thermometer?
