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 steel rod with a length of 2 m and a cross-sectional area of 4...

A steel rod with a length of

2 \text{ m}

and a cross-sectional area of

4 \text{ cm}^2

shrinks by

0.1 \text{ cm}

as the temperature decreases during the night. Determine the tension developed in the rod during the night hours if it is clamped at both ends during the day. Young modulus of steel

= 1.9 \times 10^{11} \text{ N/m}^2

Options

A $76000 \text{ N}$
B $38000 \text{ N}$
C $3800 \text{ N}$
D $19000 \text{ N}$

Correct answer

B. $38000 \text{ N}$

Step-by-step solution

Given, length of the rod,

L = 2 \text{ m}

Cross-sectional area,

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

Change in length,

\Delta L = 0.1 \text{ cm} = 10^{-3} \text{ m}

Young's modulus,

Y = 1.9 \times 10^{11} \text{ N/m}^2

The tension developed in the rod is given by the formula:

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

Substituting the given values:

F = \dfrac{1.9 \times 10^{11} \times 4 \times 10^{-4} \times 10^{-3}}{2}

F = 1.9 \times 2 \times 10^4

F = 3.8 \times 10^4 \text{ N} = 38000 \text{ N}

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