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Mechanical Properties of Solids

Modulus of Elasticity and Hooke's Law

A homogeneous block with a mass m hangs on three vertical wire

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Solving time: 3 mins

A homogeneous block with a mass $m$ hangs on three vertical wires of equal length arranged symmetrically. Find the tension of the wires if the middle wire is of steel and the other two are of copper. All the wires have the same cross-section. Consider the modulus of elasticity of steel to be double than that of copper.

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Book:

Mechanics Volume 2 (DC Pandey)

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Asher Discussed

A homogeneous block with a mass

m

hangs on three vertical wires of equal length arranged symmetrically. Find the tension of the wires if the middle wire is of steel and the other two are of copper. All the wires have the same cross-section. Consider the modulus of elasticity of steel to be double than that of copper.

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Text solutionVerified

2 T_{C} + T_{S} = m g

...(ii)

Δ l_{C} = Δ l_{s}

∴ \frac{T _{C} l _{C}}{A _{C} Y _{C}} = \frac{T _{S} l _{S}}{A _{S} Y _{S}}

∴ T_{S} = 2 T_{C}

(as

Y_{S} = 2 Y_{C}, l_{S} = l_{C}, A_{S} = A_{C}

)
or

T_{S} = 2 T_{C}

...(ii)
Solving these two equations we get,

T_{C} = \frac{m g}{4}

T_{S} = 2 T_{C}

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Question Text	A homogeneous block with a mass $m$ hangs on three vertical wires of equal length arranged symmetrically. Find the tension of the wires if the middle wire is of steel and the other two are of copper. All the wires have the same cross-section. Consider the modulus of elasticity of steel to be double than that of copper.
Topic	Mechanical Properties of Solids
Subject	Physics
Class	Class 11
Answer Type	Text solution:1
Upvotes	112

Text solutionVerified

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