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Concepts Of Physics MCQ Edition [Volume 1]

Exam: Concepts Of Physics MCQ Edition [Volume 1]
Subject: Physics
Chapter: Some Mechanical Properties of Matter

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

A load of 10 kg is suspended by a metal wire that is 3 m long and...

A load of

10 \text{ kg}

is suspended by a metal wire that is

3 \text{ m}

long and possesses a cross-sectional area of

4 \text{ mm}^2

. Determine the stress. The Young modulus of the metal is

2.0 \times 10^{11} \text{ N/m}^2

.

Options

A $2.5 \times 10^5 \text{ N/m}^2$
B $2.45 \times 10^7 \text{ N/m}^2$
C $2.5 \times 10^7 \text{ N/m}^2$
D $2.5 \times 10^6 \text{ N/m}^2$

Correct answer

B. $2.45 \times 10^7 \text{ N/m}^2$

Step-by-step solution

Given mass of the load,

m = 10 \text{ kg}

Cross-sectional area,

A = 4 \text{ mm}^2 = 4 \times 10^{-6} \text{ m}^2

Acceleration due to gravity,

g = 9.8 \text{ m/s}^2

The restoring force developed in the wire is equal to the weight of the suspended load.

F = mg = 10 \times 9.8 = 98 \text{ N}

Stress is defined as the restoring force per unit area.

\text{Stress} = \dfrac{F}{A}

\text{Stress} = \dfrac{98}{4 \times 10^{-6}} = 24.5 \times 10^6 \text{ N/m}^2

\text{Stress} = 2.45 \times 10^7 \text{ N/m}^2

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