A uniform rod of length 1 m and mas ms supported on two knife-edges placed 10 cmg cach end. A

step 1 In this cushion we have given a uniform road of length 1 meter and mass 4 kilograms and it is su

A uniform rod of length 1 m and mas ms supported on two...

A uniform rod of length $1 \mathrm{~m}$ and $\mathrm{mas}$ $m_{s}$ supported on two knife-edges placed $10 \mathrm{~cm}_{\mathrm{g}}$ cach end. A $60 \mathrm{~N}$ weight is suspended at $30 \mathrm{~cm} \mathrm{c}_{\mathrm{t}} \mathrm{c}$ one end. The reactions at the knife ed ges is (a) $60 \mathrm{~N}, 40 \mathrm{~N}$ (b) $75 \mathrm{~N}, 25 \mathrm{~N}$ (c) $65 \mathrm{~N}, 35 \mathrm{~N}$ (d) $55 \mathrm{~N}, 45 \mathrm{~N}$

A uniform rod of length $1 \mathrm{~m}$ and $\mathrm{mas}$ $m_{s}$
supported on two knife-edges placed $10 \mathrm{~cm}_{\mathrm{g}}$ cach end. A $60 \mathrm{~N}$ weight is suspended at $30 \mathrm{~cm} \mathrm{c}_{\mathrm{t}} \mathrm{c}$ one end. The reactions at the knife ed ges is
(a) $60 \mathrm{~N}, 40 \mathrm{~N}$
(b) $75 \mathrm{~N}, 25 \mathrm{~N}$
(c) $65 \mathrm{~N}, 35 \mathrm{~N}$
(d) $55 \mathrm{~N}, 45 \mathrm{~N}$

Key Concepts

Reaction Forces at Supports

Reaction forces at supports are the forces exerted by the supports to maintain equilibrium of a structure or object. These forces act in response to applied loads and are determined by applying the equations of equilibrium. Analyzing these forces helps in ensuring that structures remain stable under various loading conditions.

Center of Mass

The center of mass of a body is the point where the entire mass can be considered to be concentrated for the purpose of analyzing gravitational effects. For a uniform rod, the center of mass is located at its midpoint. Understanding the location of the center of mass is key when analyzing the distribution of weight and the resulting moments in static systems.

Static Equilibrium

Static equilibrium refers to the condition in which an object at rest has all the forces and moments acting on it balanced; that is, the sum of all forces is zero and the sum of all moments (torques) is also zero. This concept is foundational in mechanics and is used to analyze the forces acting on bodies, ensuring they do not accelerate or rotate.

Moment (Torque) Calculation

A moment, or torque, is the turning effect produced by a force acting at a distance from a pivot point. It is calculated as the product of the force and the perpendicular distance from the pivot point to the line of action of the force. In problems involving lever arms or supports, setting the sum of moments to zero is crucial for finding unknown reactions.

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