मराठी
कर्नाटक बोर्ड पी.यू.सी.पीयूसी विज्ञान इयत्ता ११

A Steel Rod is Clamped at Its Two Ends and Rests on a Fixed Horizontal Base. the Rod is Unstrained at 20°C.

Advertisements
Advertisements

प्रश्न

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.

थोडक्यात उत्तर
Advertisements

उत्तर

Given:
Temperature at which rod is resting on a fixed horizontal base without any strain, T1=20 °C. Then the rod is heated to temperature, T2 = 50 °C

​So change in temperature,ΔT =T2-T1=30°C

Coefficient of linear expansion of steel, α = 1.2 × 10–5 °C-1​ 
Let L be the length of the rod without heating and L' be the length of the rod on heating.
Let longitudinal strain developed in the rod be S.
We know that

L' =L(1+∝ΔT)

⇒ ΔL =L∝ΔT

Strain, S = `(ΔL)/L`

`=(L∝ΔT)/L`

=αΔT

⇒ S =1.2 × 10-5 ×(50-20)

=1.2 × 10-5 ×30

=1.2 × 10-5 × 30

=36 × 10-5 

S = 3.6 × 10-4

The strain of 3.6 × 10-4 will be opposite to the direction of expansion.

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 23: Heat and Temperature - Exercises [पृष्ठ १३]

APPEARS IN

एचसी वर्मा Concepts of Physics Volume 1 and 2 [English]
पाठ 23 Heat and Temperature
Exercises | Q 27 | पृष्ठ १३

संबंधित प्रश्‍न

If mercury and glass had equal coefficients of volume expansion, could we make a mercury thermometer in a glass tube?


Answer the following question.

Give an example of the disadvantages of thermal stress in practical use?


A glass flask has a volume 1 × 10−4 m3. It is filled with a liquid at 30°C. If the temperature of the system is raised to 100°C, how much of the liquid will overflow? (Coefficient of volume expansion of glass is 1.2 × 105 (°C)1 while that of the liquid is 75 × 105 (°C)1).


Solve the following problem.

A blacksmith fixes iron ring on the rim of the wooden wheel of a bullock cart. The diameter of the wooden rim and the iron ring are 1.5 m and 1.47 m respectively at room temperature of 27 °C. To what temperature the iron ring should be heated so that it can fit the rim of the wheel? (αiron = 1.2 × 10–5K–1).


A metal sphere 10.01 cm in diameter is placed on a brass ring of internal diameter 10 cm and at the same temperature of 12° C. The temperature up to which they should be heated together so that the metal sphere just passes through the ring is `[alpha_"metal"= 12 xx 10^-6//°"C" and alpha_"brass" =18 xx 10^-6//°"C"]` ____________.


A metal rod is heated to t°C. A metal rod has length, area of cross-section, Young's modulus and coefficient of linear expansion as 'L', 'A', 'Y' and 'a' respectively. When the rod is heated, the work performed is ______.


A metal rod of Young's moduls 'Y' and coefficient of linear expansion 'a' has its temeprature raised by 'Δ θ'. The linear stress to prevent the expansion of rod is ______.
(L and l is original length of rod and expansion respectively)


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)


A metal rod of length Land cross-sectional area A is heated through T °C. What is the force required to prevent the expansion of the rod lengthwise?

(Y = Young's modulus of material of the rod, α = coefficient of linear expansion of the rod.)


A bimetallic strip is made of aluminium and steel (αAl > αsteel) . On heating, the strip will ______.


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.


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).


If the length of a cylinder on heating increases by 2%, the area of its base will increase by ______.


A metal ball immersed in water weighs w1 at 0°C and w2 at 50°C. The coefficient of cubical expansion of metal is less than that of water. Then ______.


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 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) 


Which of the following correctly lists the three types of thermal expansion?


When a solid is heated, its atoms vibrate faster and move farther apart. This happens because ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×