Two halves of a round homogeneous cylinder are held together...

Two halves of a round homogeneous cylinder are held together by a thread wrapped round the cylinder with two equal weights. The complete cylinder weighs $31.4 \mathrm{~kg}$. The plane of contact of both of its halves is vertical. For equilibrium of both halves of the cylinder, the minimum value of $m$ is : (a) $\frac{2}{3} \mathrm{~g}$ (b) $3.14 \mathrm{~g}$ (c) $\frac{2}{3} \mathrm{~kg}$ (d) $31.4 \mathrm{~g}$

Two halves of a round homogeneous cylinder are held together by a thread wrapped round the cylinder with two equal weights. The complete cylinder weighs $31.4 \mathrm{~kg}$. The plane of contact of both of its halves is vertical. For equilibrium of both halves of the cylinder, the minimum value of $m$ is :
(a) $\frac{2}{3} \mathrm{~g}$
(b) $3.14 \mathrm{~g}$
(c) $\frac{2}{3} \mathrm{~kg}$
(d) $31.4 \mathrm{~g}$

Key Concepts

Tension in a Thread

Tension is the force transmitted through a string, rope, or thread when it is pulled tight by forces acting from opposite ends. In equilibrium problems like this one, the tension provided by the weights on the thread counteracts the separating forces on the two halves, ensuring that the system remains intact.

Center of Mass and Weight Distribution

The center of mass is the point in an object where the entire mass can be considered to be concentrated, and its uniform distribution in homogeneous bodies helps in simplifying the analysis of forces and torques. In this problem, understanding the weight distribution of the cylinder is crucial for determining the moments that tend to separate the halves.

Static Equilibrium

Static equilibrium is a fundamental concept in mechanics where a body remains at rest because the sum of all forces and moments (torques) acting on it is zero. This principle is used to analyze systems like the cylinder halves by ensuring that both translational and rotational forces balance out.

Force and Moment Balance

Force and moment balance refers to the requirement that, for a body to be in equilibrium, the total forces in all directions and the total moments about any axis must cancel. This concept is central when determining the conditions required to keep the cylinder halves together using an external force such as tension.

Transcript

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