A vertical metal cylinder of radius 2 cm and length 2 m is fixed at its lower end, and a load of 100 kg is placed on it. Determine the strain. The Young modulus of the metal is 2 × 10^ 11 N/m^2 .

Correct answer: D. 4 × 10^ -6 Given: Radius of the cylinder, r = 2 cm = 2 × 10^ -2 m Mass of the load, m = 100 kg Young's modulus, Y = 2 × 10^ 11 N/m^2 Acceleration due to gravity, g 10 m/s^2 The force applied on the cylinder is: F = mg = 100 × 10 = 1000 N The cross-sectional area of the cylinder is: A = π r^2 = π (2 × 10^ -2 )^2 = 4π × 10^ -4 m^2 The strain is given by the formula: Strain = Stress Y = (F)/(AY) Substituting the values: Strain = 1000 4π × 10^ -4 × 2 × 10^ 11 Strain = (1000)/(8π × 10^7) = (1)/(8π) × 10^ -4 Using π 3.14 : Strain (1)/(25.12) × 10^ -4 0.0398 × 10^ -4 4 × 10^ -6

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 vertical metal cylinder of radius 2 cm and length 2 m is fixed at...

A vertical metal cylinder of radius

2 \text{ cm}

and length

2 \text{ m}

is fixed at its lower end, and a load of

100 \text{ kg}

is placed on it. Determine the strain. The Young modulus of the metal is

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

Options

A $2 \times 10^{-6}$
B $8 \times 10^{-6}$
C $4 \times 10^{-5}$
D $4 \times 10^{-6}$

Correct answer

D. $4 \times 10^{-6}$

Step-by-step solution

Given:
Radius of the cylinder,

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

Mass of the load,

m = 100 \text{ kg}

Young's modulus,

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

Acceleration due to gravity,

g \approx 10 \text{ m/s}^2

The force applied on the cylinder is:

F = mg = 100 \times 10 = 1000 \text{ N}

The cross-sectional area of the cylinder is:

A = \pi r^2 = \pi (2 \times 10^{-2})^2 = 4\pi \times 10^{-4} \text{ m}^2

The strain is given by the formula:

\text{Strain} = \dfrac{\text{Stress}}{Y} = \dfrac{F}{AY}

Substituting the values:

\text{Strain} = \dfrac{1000}{4\pi \times 10^{-4} \times 2 \times 10^{11}}

\text{Strain} = \dfrac{1000}{8\pi \times 10^7} = \dfrac{1}{8\pi} \times 10^{-4}

Using

\pi \approx 3.14

\text{Strain} \approx \dfrac{1}{25.12} \times 10^{-4} \approx 0.0398 \times 10^{-4} \approx 4 \times 10^{-6}

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