A ball of mass 1 kg hangs in equilibrium from two strings O...

A ball of mass $1 \mathrm{~kg}$ hangs in equilibrium from two strings $O A$ and $O B$ as shown in figure. What are the tensions in strings $O A$ and $O B ?$ (Take $g=10 \mathrm{~ms}^{-2}$ ) (a) $5 \mathrm{~N}$, zero (b) Zero, $\mathrm{N}$ (c) $5 \mathrm{~N}, 5 \sqrt{3} \mathrm{~N}$ (d) $5 \sqrt{3} \mathrm{~N}, 5 \mathrm{~N}$

A ball of mass $1 \mathrm{~kg}$ hangs in equilibrium from two strings $O A$ and $O B$ as shown in figure. What are the tensions in strings $O A$ and $O B ?$ (Take $g=10 \mathrm{~ms}^{-2}$ )
(a) $5 \mathrm{~N}$, zero
(b) Zero, $\mathrm{N}$
(c) $5 \mathrm{~N}, 5 \sqrt{3} \mathrm{~N}$
(d) $5 \sqrt{3} \mathrm{~N}, 5 \mathrm{~N}$

Key Concepts

Resolving Forces Into Components

Forces acting at angles can be broken down into perpendicular components using trigonometric functions like sine and cosine. This method simplifies the process of applying the equilibrium conditions in each direction (horizontal and vertical) independently.

Application of Trigonometry in Equilibrium

Trigonometry is used to relate the angles of the strings to the magnitudes of the force components. By setting up equations based on the sine and cosine of the angles, one can solve for the unknown tensions ensuring that the net force in each direction is zero.

Tension Forces in Strings

Tension is the pulling force transmitted along the length of a string or rope. When an object is suspended by multiple strings, the tension in each string can be determined by analyzing the balance of forces and resolving them along the relevant directions.

Free-Body Diagram

A free?body diagram is a graphical illustration used to visualize all the forces acting upon an object. In problems involving multiple forces, such as tensions in strings, drawing a free-body diagram helps in identifying and balancing the forces correctly.

Static Equilibrium

In statics, an object is in equilibrium when the sum of all forces acting on it is zero. This means there is no net force in any direction, allowing the object to remain at rest. The conditions for equilibrium are applied to both horizontal and vertical force components.

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