Assertion: A block of mass m is at rest on a inclined...

Assertion: A block of mass $m$ is at rest on a inclined surface of inclination $\theta$. Normal contact force between block and surface is $m g \cos \theta$. Reason: If block of mass $m$ is at rest on inclined surface of inclination $\theta$. Friction force on the block is $m g \sin \theta$ (A) $\mathrm{A}$ (B) $\mathrm{B}$ (C) $\mathrm{C}$ (D) D

Assertion: A block of mass $m$ is at rest on a inclined surface of inclination $\theta$. Normal contact force between block and surface is $m g \cos \theta$.
Reason: If block of mass $m$ is at rest on inclined surface of inclination $\theta$. Friction force on the block is $m g \sin \theta$
(A) $\mathrm{A}$
(B) $\mathrm{B}$
(C) $\mathrm{C}$
(D) D

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Key Concepts

Equilibrium on an Incline

This concept describes the condition where the net force acting on an object on an inclined plane is zero, meaning that the component of gravity parallel to the incline is exactly balanced by the static friction force. This state ensures that the object remains at rest despite the gravitational pull.

Static Friction

Static friction is the force that resists the initiation of motion between two contacting surfaces. It adjusts its magnitude to counterbalance any applied forces up to a maximum limit determined by the product of the normal force and the coefficient of static friction, and it prevents movement when the object is at rest.

Force Resolution on an Inclined Plane

This concept involves breaking down the gravitational force acting on an object into components parallel and perpendicular to the surface of an incline. The perpendicular component (mg cos?) influences the normal force, and the parallel component (mg sin?) is what tends to cause the block to slide down the plane.

Normal Force

The normal force is the support force exerted by a surface perpendicular to an object in contact with it. For an object placed on an inclined plane, this force counteracts the perpendicular component of gravity, and its magnitude is derived from mg cos? under equilibrium conditions.

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