Home
Class 11
PHYSICS
Two rods of equal cross sections, one of...

Two rods of equal cross sections, one of copper and the other of steel, are joined to form a composite rod of length 2.0 m at `20^@C`, the length of the copper rod is 0.5 m. When the temperature is raised to `120^@C`, the length of composite rod increases to 2.002m. If the composite rod is fixed between two rigid walls and thus not allowed to expand, it is found that the lengths of the component rods also do not change with increase in temperature. Calculate Young's moulus of steel. (The coefficient of linear expansion of copper, `alpha_c=1.6xx10^(-5@)C` and Young's modulus of copper is `1.3xx10^(13)N//m^(2)`).

Text Solution

AI Generated Solution

To solve the problem, we will follow these steps: ### Step 1: Understand the Problem We have two rods, one made of copper and the other made of steel, which are joined together. The total length of the composite rod is 2.0 m, with the copper rod being 0.5 m long. We need to calculate the Young's modulus of steel given that the rods do not change in length when the temperature is raised from 20°C to 120°C. ### Step 2: Calculate the Change in Length of the Copper Rod The change in length of the copper rod (\( \Delta L_c \)) can be calculated using the formula: \[ ...
Promotional Banner

Topper's Solved these Questions

  • CALORIMETRY

    CENGAGE PHYSICS ENGLISH|Exercise Exercise 1.1|23 Videos

  • CALORIMETRY

    CENGAGE PHYSICS ENGLISH|Exercise Exercise 1.2|22 Videos

  • BASIC MATHEMATICS

    CENGAGE PHYSICS ENGLISH|Exercise Exercise 2.6|20 Videos

  • CENTRE OF MASS

    CENGAGE PHYSICS ENGLISH|Exercise INTEGER_TYPE|1 Videos

Similar Questions

Explore conceptually related problems

A composite rod is made by joining a copper rod, end to end, with a second rod of different material but of the same area of cross section. At 25^(@)C , the composite rod is 1 m long and the copper rod is 30 cm long. At 125^(@)C the length of the composite rod increases by 1.91 mm . When the composite rod is prevented from expanding by holding it between two rigid walls, it is found that the constituent rods have remained unchanged in length inspite of rise of temperature. Find young's modulus and the coefficient of linear expansion of the second rod (Y of copper =1.3xx10^(10) N//m^(2) and a of copper =17xx10^(-6)//K ).

A composite rod is made by joining a copper rod, end to end, with a second rod of different material but of the same area of cross section. At 25^(@)C , the composite rod is 1 m long and the copper rod is 30 cm long. At 125^(@)C the length of the composte rod increases by 1.91 mm . When the composite rod is prevented from expanding by bolding it between two rigid walls, it is found that the constituent reds have remained unchanged in length in splite of rise of temperature. Find yong's modulus and the coefficient of linear expansion of the second red (Y of copper =1.3xx10^(10) N//m^(2) and a of copper =17xx10^(-6)//K ).

A rod of length / and radius r is held between two rigid walls so that it is not allowed to expand. If its temperature is increased, then the force developed in it is proportional to

A brass rod of length 1 m is fixed to a vertical wall at one end, with the other end keeping free to expand. When the temperature of the rod is increased by 120^@C , the length increases by 3 cm . What is the strain?

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 clapms? Area of cross section of the rod = 2.00 mm^2 . Coefficient of linear expansion of steel = 12.0 xx 10^(-6)C^(-1) and Young's modulus of steel 2.00 xx 10^(11) N m^(-2) .

The temperature gradient in a rod of 0.5 m length is 80^(@)C//m . It the temperature of hotter end of the rod is 30^(@)C , then the temperature of the cooler end is

A steel tape 1m long is correctly calibrated for a temperature of 27^(@)C . The length of a steel rod measured by this tape is found to be 63.0cm on a hot day when the temperature is 45.0^(@)C . What is the acutual length of the steel rod on that day? what is the length of the same steel rod on a day when the temperature is 27.0^(@)C ? coefficient of linear expansion of steel = 1.20xx10^(-5) .^(@)C^(-1) .

The length of a rod is (11.05+-0.05)cm . What is the length of two such rods?

On heating the metal rod of length 2m from 0°C to 50°C , its length is increased by 0.1 cm. the coeffecient of linear expansion of metal rod is

A steel rod of length 1 m is heated from 25^@ "to" 75^@ C keeping its length constant. The longitudinal strain developed in the rod is ( Given, coefficient of linear expansion of steel = 12 xx 10^-6//^@ C ).