Two persons are pulling a rope towards themselves. Each person applies a force of 100 N on the rope. Determine the Young modulus of the rope's material if it extends in length by 1 cm . The original length of the rope

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Quantrex Academy · Accepted Answer

Correct answer: A. 1 × 10^8 N/m^2

Since two persons are pulling the rope from opposite ends with a force of

100 \text{ N}

each, the tension developed in the rope is

F = 100 \text{ N}

.

The given parameters are

L = 2 \text{ m}

,

\Delta L = 1 \text{ cm} = 10^{-2} \text{ m}

, and

A = 2 \text{ cm}^2 = 2 \times 10^{-4} \text{ m}^2

.

The Young modulus is given by

Y = \dfrac{F L}{A \Delta L}

.

Substituting the values:

Y = \dfrac{100 \times 2}{2 \times 10^{-4} \times 10^{-2}}

Y = \dfrac{200}{2 \times 10^{-6}}

Y = 1 \times 10^8 \text{ N/m}^2

Two persons are pulling a rope towards themselves. Each person...

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