A uniform rod A B of mass 2 kg and length 1 m is placed on a wedge O. To keep the rod horizont

step 1 In this question, we have a uniform rod of mass M equals to 2 KG and length L equals to 1 meter

A uniform rod A B of mass 2 kg and length 1 m is placed on...

A uniform rod $A B$ of mass $2 \mathrm{~kg}$ and length $1 \mathrm{~m}$ is placed on a wedge $\mathrm{O}$. To keep the rod horizontal, its end $\mathrm{A}$ is tied with a thread and the spring has tension $6 \mathrm{~N}$. The reaction of support $\mathrm{O}$ on the rod when the thread is burnt is (a) $15 \mathrm{~N}$ (b) $40 \mathrm{~N}$ (c) $20 \mathrm{~N}$ (d) $25 \mathrm{~N}$

A uniform rod $A B$ of mass $2 \mathrm{~kg}$ and length $1 \mathrm{~m}$ is placed on a wedge $\mathrm{O}$. To keep the rod horizontal, its end $\mathrm{A}$ is tied with a thread and the spring has tension $6 \mathrm{~N}$. The reaction of support $\mathrm{O}$ on the rod when the thread is burnt is
(a) $15 \mathrm{~N}$
(b) $40 \mathrm{~N}$
(c) $20 \mathrm{~N}$
(d) $25 \mathrm{~N}$

Key Concepts

Reaction Force

Reaction forces are the forces exerted by supports or surfaces to counteract external loads. In the context of a rod resting on a wedge, understanding how the reaction force is determined by balancing the external forces and torques is fundamental for analyzing the stability and support conditions of the rod.

Static Equilibrium

In statics, an object is in equilibrium when the sum of all forces and the sum of all moments (torques) acting on it are zero. This principle is essential for analyzing the stability of structures and mechanisms, such as a rod on a wedge, and is used to set up equations for force balance and moment balance.

Torque (Moment of Force)

Torque is the rotational effect created by a force acting at a distance from a pivot point. In problems involving beams or rods, calculating torques about a specific point helps determine how forces are distributed along the structure, ensuring that the net moment is zero in a state of equilibrium.

Center of Mass

The center of mass is the point at which the mass of an object is considered to be concentrated for the purposes of analysis. For uniform objects like the rod, the weight is assumed to act at the center of mass, which is crucial when determining the moments generated by gravitational forces in equilibrium problems.

Force Resolution

Analyzing forces often requires breaking them down into components along chosen axes (typically horizontal and vertical). This process of resolution simplifies the application of equilibrium conditions, enabling a clearer view of how individual contributions of different forces combine to satisfy both translational and rotational balance.

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