Two bodies of masses 1 kg and 2 kg are connected by a metal wire shown in figure. A force of 1

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Two bodies of masses 1 kg and 2 kg are connected by a...

Two bodies of masses $1 \mathrm{~kg}$ and $2 \mathrm{~kg}$ are connected by a metal wire shown in figure. A force of $10 \mathrm{~N}$ is applied on the body of mass $2 \mathrm{~kg}$. The breaking stress of metal wire is $2 \times 10^{9} \mathrm{~N} / \mathrm{m}^{2}$. What should be minimum radius of the wire used, if it is not to break? (a) $0.23 \times 10^{-4} \mathrm{~m}$ (b) $4 \times 10^{-1} \mathrm{~m}$ (c) $5 \times 10^{-4} \mathrm{~m}$ (d) $5.2 \times 10^{-i} \mathrm{~m}$

Two bodies of masses $1 \mathrm{~kg}$ and $2 \mathrm{~kg}$ are connected by a metal wire shown in figure. A force of $10 \mathrm{~N}$ is applied on the body of mass $2 \mathrm{~kg}$. The breaking stress of metal wire is $2 \times 10^{9} \mathrm{~N} / \mathrm{m}^{2}$.
What should be minimum radius of the wire used, if it is not to break?
(a) $0.23 \times 10^{-4} \mathrm{~m}$
(b) $4 \times 10^{-1} \mathrm{~m}$
(c) $5 \times 10^{-4} \mathrm{~m}$
(d) $5.2 \times 10^{-i} \mathrm{~m}$

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Key Concepts

Newton's Second Law

Newton's Second Law states that the net force on an object equals the mass of the object multiplied by its acceleration (F = ma). This concept is essential in determining the acceleration of connected bodies when a force is applied to one of them.

Tension in a Connecting Wire

Tension is the force transmitted through a string or wire when forces are applied at its ends. In a system where two bodies are connected, calculating the tension in the wire is crucial as it determines the force that the wire must withstand, thereby linking dynamics and material strength.

Stress and Tensile Strength

Stress is defined as the force applied per unit area (? = F/A). The tensile (or breaking) stress is the maximum stress that a material can withstand before it fails. This concept is key to ensuring that the applied force does not exceed the material's capacity, which would lead to breakage.

Area of a Circular Cross-section

The area of a circular cross-section is given by the formula A = ?r², where r is the radius of the wire. This calculation is necessary to determine the minimum wire radius required so that the stress (force divided by area) remains below the material's breaking stress.

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