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Two uniform rods ab and bc have youngs modulli1.2 and 1.5 respectively. if coefficient of linear expansion of ab is 1.5 and both have equal area of cross section , then coefficient of linear expansion of bc , for which there is no shift of junction at which they are joines ,at all temperature is?
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Two uniform rods ab and bc have youngs modulli1.2 and 1.5 respectively...
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Two uniform rods ab and bc have youngs modulli1.2 and 1.5 respectively...
The coefficient of linear expansion is a measure of how much a material expands or contracts when subjected to a change in temperature. It is denoted by the symbol α and is defined as the change in length per unit length per degree Celsius.
Given that the coefficient of linear expansion of rod AB is 1.5, we can calculate the change in length of rod AB using the formula:
ΔL_AB = α_AB * L_AB * ΔT
where ΔL_AB is the change in length of rod AB, α_AB is the coefficient of linear expansion of rod AB, L_AB is the original length of rod AB, and ΔT is the change in temperature.
Similarly, for rod BC, the change in length can be calculated using the formula:
ΔL_BC = α_BC * L_BC * ΔT
where ΔL_BC is the change in length of rod BC, α_BC is the coefficient of linear expansion of rod BC, and L_BC is the original length of rod BC.
Since the junction between rod AB and rod BC does not shift at any temperature, the change in length of rod BC should be equal to the change in length of rod AB. Therefore, we can equate the two expressions for ΔL_AB and ΔL_BC:
α_AB * L_AB * ΔT = α_BC * L_BC * ΔT
Cancelling ΔT from both sides of the equation, we get:
α_AB * L_AB = α_BC * L_BC
Since both rods have equal cross-sectional areas, their lengths can be expressed in terms of their volumes:
L_AB = V_AB / A
L_BC = V_BC / A
where V_AB and V_BC are the volumes of rod AB and rod BC, respectively, and A is the cross-sectional area.
Substituting these expressions into the equation, we have:
α_AB * (V_AB / A) = α_BC * (V_BC / A)
Simplifying the equation, we find:
α_BC = (α_AB * V_AB) / V_BC
Since the Young's modulus of rod AB is 1.2 and the Young's modulus of rod BC is 1.5, we can express their volumes in terms of their lengths and Young's moduli:
V_AB = (A * L_AB) / 1.2
V_BC = (A * L_BC) / 1.5
Substituting these expressions into the equation for α_BC, we get:
α_BC = (α_AB * V_AB) / V_BC
= (α_AB * (A * L_AB) / 1.2) / ((A * L_BC) / 1.5)
= (α_AB * L_AB * 1.5) / (L_BC * 1.2)
Simplifying further, we find:
α_BC = (1.5 * α_AB) / 1.2
Therefore, the coefficient of linear expansion of rod BC, for which there is no shift of the junction, is given by:
α_BC = (1.5 * α_AB) / 1.2
In this case, we have α_AB = 1.5, so substituting this value into the equation, we get:
α_BC = (1.5 * 1.5) / 1.2
= 1.875 / 1.2
=
Given that the coefficient of linear expansion of rod AB is 1.5, we can calculate the change in length of rod AB using the formula:
ΔL_AB = α_AB * L_AB * ΔT
where ΔL_AB is the change in length of rod AB, α_AB is the coefficient of linear expansion of rod AB, L_AB is the original length of rod AB, and ΔT is the change in temperature.
Similarly, for rod BC, the change in length can be calculated using the formula:
ΔL_BC = α_BC * L_BC * ΔT
where ΔL_BC is the change in length of rod BC, α_BC is the coefficient of linear expansion of rod BC, and L_BC is the original length of rod BC.
Since the junction between rod AB and rod BC does not shift at any temperature, the change in length of rod BC should be equal to the change in length of rod AB. Therefore, we can equate the two expressions for ΔL_AB and ΔL_BC:
α_AB * L_AB * ΔT = α_BC * L_BC * ΔT
Cancelling ΔT from both sides of the equation, we get:
α_AB * L_AB = α_BC * L_BC
Since both rods have equal cross-sectional areas, their lengths can be expressed in terms of their volumes:
L_AB = V_AB / A
L_BC = V_BC / A
where V_AB and V_BC are the volumes of rod AB and rod BC, respectively, and A is the cross-sectional area.
Substituting these expressions into the equation, we have:
α_AB * (V_AB / A) = α_BC * (V_BC / A)
Simplifying the equation, we find:
α_BC = (α_AB * V_AB) / V_BC
Since the Young's modulus of rod AB is 1.2 and the Young's modulus of rod BC is 1.5, we can express their volumes in terms of their lengths and Young's moduli:
V_AB = (A * L_AB) / 1.2
V_BC = (A * L_BC) / 1.5
Substituting these expressions into the equation for α_BC, we get:
α_BC = (α_AB * V_AB) / V_BC
= (α_AB * (A * L_AB) / 1.2) / ((A * L_BC) / 1.5)
= (α_AB * L_AB * 1.5) / (L_BC * 1.2)
Simplifying further, we find:
α_BC = (1.5 * α_AB) / 1.2
Therefore, the coefficient of linear expansion of rod BC, for which there is no shift of the junction, is given by:
α_BC = (1.5 * α_AB) / 1.2
In this case, we have α_AB = 1.5, so substituting this value into the equation, we get:
α_BC = (1.5 * 1.5) / 1.2
= 1.875 / 1.2
=
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Two uniform rods ab and bc have youngs modulli1.2 and 1.5 respectively. if coefficient of linear expansion of ab is 1.5 and both have equal area of cross section , then coefficient of linear expansion of bc , for which there is no shift of junction at which they are joines ,at all temperature is?
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Two uniform rods ab and bc have youngs modulli1.2 and 1.5 respectively. if coefficient of linear expansion of ab is 1.5 and both have equal area of cross section , then coefficient of linear expansion of bc , for which there is no shift of junction at which they are joines ,at all temperature is? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Two uniform rods ab and bc have youngs modulli1.2 and 1.5 respectively. if coefficient of linear expansion of ab is 1.5 and both have equal area of cross section , then coefficient of linear expansion of bc , for which there is no shift of junction at which they are joines ,at all temperature is? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two uniform rods ab and bc have youngs modulli1.2 and 1.5 respectively. if coefficient of linear expansion of ab is 1.5 and both have equal area of cross section , then coefficient of linear expansion of bc , for which there is no shift of junction at which they are joines ,at all temperature is?.
Two uniform rods ab and bc have youngs modulli1.2 and 1.5 respectively. if coefficient of linear expansion of ab is 1.5 and both have equal area of cross section , then coefficient of linear expansion of bc , for which there is no shift of junction at which they are joines ,at all temperature is? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Two uniform rods ab and bc have youngs modulli1.2 and 1.5 respectively. if coefficient of linear expansion of ab is 1.5 and both have equal area of cross section , then coefficient of linear expansion of bc , for which there is no shift of junction at which they are joines ,at all temperature is? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two uniform rods ab and bc have youngs modulli1.2 and 1.5 respectively. if coefficient of linear expansion of ab is 1.5 and both have equal area of cross section , then coefficient of linear expansion of bc , for which there is no shift of junction at which they are joines ,at all temperature is?.
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