Advertisements
Advertisements
प्रश्न
A steel wire of cross-sectional area 0.5 mm2 is held between two fixed supports. If the wire is just taut at 20°C, determine the tension when the temperature falls to 0°C. Coefficient of linear expansion of steel is 1.2 × 10–5 °C–1 and its Young's modulus is 2.0 × 10–11 Nm–2.
उत्तर
Given:
Cross-sectional area of the steel wire, A = 0.5 mm2 = 0.5 × 10–6 m2
The wire is taut at a temperature, T1 = 20 °C,
After this, the temperature is reduced to T2 = 0 °C
So, the change in temperature, Δθ = T1-T2 = 20 °C
Coefficient of linear expansion of steel, α = 1.2 ×10–5 °C-1
Young's modulus, γ = 2 ×1011 Nm-2
Let L be the initial length of the steel wire and L' be the length of the steel wire when temperature is reduced to 0°C.
Decrease in length due to compression, ΔL =L' - L = LαΔθ ...(1)
Let the tension applied be F.
`γ = "stress"/"strain" =("F"/"A")/((triangle"L")/"L")`
`=> γ = "F"/"A" xx "L"/(triangle"L")`
`=> triangle"L" = "FL"/("A"gamma)` ..(2)
Change in length due to tension produced is given by (1) and (2).
So, on equating (1) and (2), we get:
`"L"αΔθ ="FL"/("A"gamma)`
⇒ F = αΔθAγ
= 1.2 × 10-5 × (20-0) × 0.5 ×10-6 × 2 ×1011
= 1.2 × 20
⇒ F = 24 N
Therefore, the tension produced when the temperature falls to 0°C
APPEARS IN
संबंधित प्रश्न
Two copper spheres of radii 6 cm and 12 cm respectively are suspended in an evacuated enclosure. Each of them are at a temperature 15°C above the surroundings. The ratio of their rate of loss of heat is.................
- 2:1
- 1:4
- 1:8
- 8:1
The light from the Sun is found to have a maximum intensity near the wavelength of 470 nm. Assuming the surface of the Sun as a black body, the temperature of the Sun is _____________.
[Wien's constant b = 2 .898 x l0- 3mK]
A metal ball cools from 64 °C to 50 °C in 10 minutes and to 42 °C in next 10 minutes. The ratio of rates of fall of temperature during the two intervals is _______.
The susceptibility of magnesium at 300K is 1.2 x 10-5. At what temperature will the susceptibility increase to 1.8 X 10-5?
The substance which allows heat radiations to pass through is _______.
(A) iron
(B) water vapour
(C) wood
(D) dry air
A body cools from 80° C to 70° C in 5 minutes and to 62° C in the next 5 minutes. Calculate the temperature of the surroundings.
The length of a brass rod is found to be less on a hot summer day than on a cold winter day as measured by the same aluminium scale. Can we conclude that brass shrinks on heating?
A spinning wheel A is brought in contact with another wheel B, initially at rest. Because of the friction at contact, the second wheel also starts spinning. Which of the following energies of the wheel B increases?
(a) Kinetic
(b) Total
(c) Mechanical
(d) Internal
A person's skin is more severely burnt when put in contact with 1 g of steam at 100°C than when put in contact with 1 g of water at 100°C. Explain
The atmospheric temperature in the cities on sea-coast change very little. Explain
Should a thermometer bulb have large heat capacity or small heat capacity?
Water equivalent of a body is measured in ___________ .
Two bodies at different temperatures are mixed in a calorimeter. Which of the following quantities remains conserved?
The heat capacity of a body depends on
(a) the heat given
(b) the temperature raised
(c) the mass of the body
(d) the material of the body
Temperature and Heat are ______
Two tumblers of A and B have water at 50°C temperature. If the water from A and B is poured into tumbler C. The temperature of C is ______.
Temperature in the form of energy.
Two identical beakers A and B contain equal volumes of two different liquids at 60°C each and is left to cool down. Liquid in A has a density of 8 × 102 kg/m3 and specific heat of 2000 J kg-1 K-1 while the liquid in B has a density of 103 kg m-3 and specific heat of 4000 J kg-1 K-1. Which of the following best describes their temperature versus time graph schematically? (assume the emissivity of both the beakers to be the same.)
An earthen pitcher loses 1 gm of water per minute due to evaporation. If the water equivalent of the pitcher is 0.5 kg and the pitcher contains 9.5 kg of water, calculate the time required for the water in a pitcher to cool to 28°C from the original temperature of 30°C. Neglect radiation effects. The latent heat of vaporization in this range of temperature is 580 Cal/gm and the specific heat of water is 1 Cal/gm°C.
