A given object takes n times more time to slide down 45^∘ rough inclined plane as it takes to sl

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A given object takes n times more time to slide down 45^∘...

A given object takes $n$ times more time to slide down $45^{\circ}$ rough inclined plane as it takes to slide down a perfectly smooth $45^{\circ}$ incline. The coefficient of kinetic friction between the object and the incline is a. $\frac{1}{2-n^{2}}$ b. $1-\frac{1}{n^{2}}$ c. $\sqrt{1-\frac{1}{n^{2}}}$ d. $\sqrt{\frac{1}{1-n^{2}}}$

A given object takes $n$ times more time to slide down $45^{\circ}$ rough inclined plane as it takes to slide down a perfectly smooth $45^{\circ}$ incline. The coefficient of kinetic friction between the object and the incline is
a. $\frac{1}{2-n^{2}}$
b. $1-\frac{1}{n^{2}}$
c. $\sqrt{1-\frac{1}{n^{2}}}$
d. $\sqrt{\frac{1}{1-n^{2}}}$

Key Concepts

Kinematics in Uniformly Accelerated Motion

Kinematics deals with the motion of objects without considering the forces that cause this motion. For objects sliding down inclines under constant acceleration, kinematic equations are used to relate displacement, time, and acceleration, which is critical when comparing the motion under different frictional conditions.

Inclined Plane Dynamics

This concept involves analyzing the forces acting on an object on an inclined surface, where the gravitational force is decomposed into components parallel and perpendicular to the plane. Understanding these components is crucial for solving problems related to motion on slopes, especially when considering the effect of friction.

Newton's Second Law of Motion

Newton's Second Law relates the net force acting on an object to its mass and acceleration. For an object on an inclined plane, this principle helps establish equations for motion by accounting for gravitational components and frictional forces, thereby allowing one to derive expressions for acceleration.

Kinetic Friction

Kinetic friction is the resistive force that opposes the motion of an object sliding over a surface. It is characterized by the coefficient of kinetic friction and the normal force, and plays a key role in modifying the net force and the resulting acceleration of an object on an incline.

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