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4 years ago

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A steel wire of length 4.7 m and cross section 3 x 103 m2 stretches by the same amount as a copper wire of length 3.5 m and cros

s section 4 x 10-5 m2 under a given load. What is the ratio of the Young's modulus of steel to that of copper? (a) 3.83 x 103 (b) 1.46 x 10-2 (d) 5.85 x 10-3 (c) 1.79 x 10-2 2.

1 answer:

EleoNora [17]4 years ago

5 0

Answer:

The ratio of the young's modulus of steel and copper is $1.79\times10^{-2}$

(c) is correct option.

Explanation:

Given that,

Length of steel wire = 4.7 m

Cross section $A = 3\times10^{-3}\ m^2$

Length of copper wire = 3.5 m

Cross section $A = 4\times10^{-5}\ m^2$

We need to calculate the ratio of young's modulus of steel and copper

Using formula of young's modulus for steel wire

$Y=\dfrac{\dfrac{F}{A}}{\dfrac{\Delta l}{l}}$

$Y_{s}=\dfrac{Fl_{s}}{A_{s}\Delta l}$ ....(I)

The young's modulus for copper wire

$Y_{c}=\dfrac{Fl_{c}}{A_{c}\Delta l}$ ....(II)

From equation (I) and (II)

The ratio of the young's modulus of steel and copper

$\dfrac{Y_{s}}{Y_{c}}=\dfrac{\dfrac{Fl_{s}}{A_{s}\Delta l}}{\dfrac{Fl_{c}}{A_{c}\Delta l}}$

$\dfrac{Y_{s}}{Y_{c}}=\dfrac{A_{c}\times l_{s}}{A_{s}\times l_{c}}$

$\dfrac{Y_{s}}{Y_{c}}=\dfrac{4\times10^{-5}\times4.7}{3\times10^{-3}\times3.5}$

$\dfrac{Y_{s}}{Y_{c}}=1.79\times10^{-2}$

Hence, The ratio of the young's modulus of steel and copper is $1.79\times10^{-2}$

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Let suppose that changes in potential energy can be neglected. According to the Work-Energy Theorem, an external conservative force generates a change in the state of motion of the object, that is a change in kinetic energy. This phenomenon is describe by the following mathematical model:

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Where:

$W_{F}$ - Work done by the external force, measured in joules.

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After using the definition of translational kinetic energy, the previous expression is now expanded as a function of mass and initial and final speeds of the object:

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$m$ - Mass of the object, measured in kilograms.

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Now, each speed is the magnitude of respective velocity vector:

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The work done by the force is 820.745 joules.

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