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Concepts Of Physics MCQ Edition [Volume 1]PhysicsSome Mechanical Properties of Matter

As a metal wire is stretched by a load, the fractional change in its volume V V is proportional to

Options

  1. Al l
  2. B( l l )^2
  3. Cl l
  4. Dl l

Correct answer

D. l l

Step-by-step solution

Volume of a cylindrical wire is V = r^2 l Differentiating to find the fractional change in volume: V V = 2 r r + l l Poisson's ratio is defined as = - r / r l / l r r = - l l Substituting this into the expression for fractional change in volume: V V = -2 l l + l l = (1 - 2 ) l l Since is a constant for a given material, (1 - 2 ) is constant. Therefore, V V l l

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