Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
As per the 1st observation, we can infer that linear expansion α is,
α = `(∆l)/(l∆t)`
= `(4 xx 10^-4)/(2 xx 10)`
= `2 xx 10^(-5^circ) C^-1`
For observation no. 2,
α = `(∆l)/(l∆t)`
`∆l = αl∆t`
= `2 xx 10^-5 xx 1 xx 10`
= `2 xx 10^-4 m`
But given value is `∆l = 4 xx 10^-4 m`
So, 2nd observation is incorrect.
For observation no. 3,
α = `(∆l)/(l∆t)`
`∆l = αl∆t`
= `2 xx 10^-5 xx 2 xx 20`
= `8 xx 10^-4 m`
But the given value is `∆l = 2 xx 10^-4 m`
So, 3rd observation is incorrect.
For observation no. 4,
α = `(∆l)/(l∆t)`
`∆l = αl∆t`
= `2 xx 10^-5 xx 3 xx 10`
= `6 xx 10^-4 m`
Here the obtained value is the same as the given value.
So, the 4th observation is correct.
APPEARS IN
संबंधित प्रश्न
The coefficient of volume expansion of glycerin is 49 × 10–5 K–1. What is the fractional change in its density for a 30 °C rise in temperature?
Show that the moment of inertia of a solid body of any shape changes with temperature as I = I0 (1 + 2αθ), where I0 is the moment of inertia at 0°C and α is the coefficient of linear expansion of the solid.
Answer the following question.
Derive the relation between three coefficients of thermal expansion.
Answer the following question.
State applications of thermal expansion.
An iron plate has a circular hole of a diameter 11 cm. Find the diameter of the hole when the plate is uniformly heated from 10° C to 90° C.`[alpha = 12 xx 10^-6//°"C"]`
A metal rod of cross-sectional area 3 × 10-6 m2 is suspended vertically from one end has a length 0.4 m at 100°C. Now the rod is cooled upto 0°C, but prevented from contracting by attaching a mass 'm' at the lower end. The value of 'm' is ______.
(Y = 1011 N/m2, coefficient of linear expansion = 10-5/K, g = 10m/s2)
An aluminium sphere is dipped into water. Which of the following is true?
Find out the increase in moment of inertia I of a uniform rod (coefficient of linear expansion α) about its perpendicular bisector when its temperature is slightly increased by ∆T.
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 ______.
A disc is rotating freely about its axis. The percentage change in angular velocity of a disc if temperature decreases by 20°C is ______.
(coefficient of linear expansion of material of disc is 5 × 10-4/°C)
If the temperature of the sun were to increase from T to 2T and its radius from R to 2R, then the ratio of the radiant energy received on earth to what it was previously will be ______.
A glass flask is filled up to a mark with 50 cc of mercury at 18°C. If the flask and contents are heated to 38°C, how much mercury will be above the mark? (α for glass is 9 × 10-6/°C and coefficient of real expansion of mercury is 180 × 10-6/°C)
A clock with an iron pendulum keeps the correct time at 15°C. If the room temperature is 20°C, the error in seconds per day will be near ______.
(coefficient of linear expansion of iron is 1.2 × 10-5/°C)
A metal rod Y = 2 × 1012 dyne cm-2 of coefficient of linear expansion 1.6 × 10-5 per °C has its temperature raised by 20°C. The linear compressive stress to prevent the expansion of the rod is ______.
