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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 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 stress. The Young modulus of the metal is

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

.

Options

A $7.96 \times 10^5 \text{ N/m}^2$
B $7.96 \times 10^6 \text{ N/m}^2$
C $3.98 \times 10^5 \text{ N/m}^2$
D $1.59 \times 10^6 \text{ N/m}^2$

Correct answer

A. $7.96 \times 10^5 \text{ N/m}^2$

Step-by-step solution

The stress on the cylinder is given by the ratio of the applied force to the cross-sectional area.

Force applied by the load,

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

Cross-sectional area,

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

\text{Stress} = \dfrac{F}{A} = \dfrac{1000}{4\pi \times 10^{-4}}

\text{Stress} = \dfrac{10^7}{4\pi} \approx 7.96 \times 10^5 \text{ N/m}^2

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