A block slides down an inclined plane of slope of angle θwith a constant velocity v . It is then

step 1 In this question it is told that a block slides down on an inclined plane with a constant veloci

A block slides down an inclined plane of slope of angle...

A block slides down an inclined plane of slope of angle $\theta$ with a constant velocity $v .$ It is then projected up the plane with an initial velocity $u$. The distance upto which it will rise before coming to rest is (a) $\frac{u^{2}}{4 g \sin \theta}$ (b) $\frac{u}{4 g \sin \theta}$ (c) $\frac{u^{2} \sin \theta}{4 g}$ (d) $\frac{u \sin \theta}{4 g}$

A block slides down an inclined plane of slope of angle $\theta$ with a constant velocity $v .$ It is then projected up the plane with an initial velocity $u$. The distance upto which it will rise before coming to rest is
(a) $\frac{u^{2}}{4 g \sin \theta}$
(b) $\frac{u}{4 g \sin \theta}$
(c) $\frac{u^{2} \sin \theta}{4 g}$
(d) $\frac{u \sin \theta}{4 g}$

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Key Concepts

Kinematics of Uniformly Accelerated Motion

Kinematic equations describe the motion of objects under uniform acceleration (or deceleration). When an object is projected upward along an inclined plane, the net retarding force (from both the gravitational component and friction) results in a uniform deceleration. Utilizing equations such as u² = 2ad allows us to calculate distances traveled before the object comes to rest.

Force Resolution on an Inclined Plane

In inclined plane problems, the gravitational force acting on an object is typically resolved into components parallel and perpendicular to the plane. The parallel component (mg sin?) drives the motion down the plane, while the perpendicular component (mg cos?) affects the normal force. This resolution is critical for analyzing the dynamics of objects on a slope, especially when other forces such as friction are present.

Friction and Equilibrium Conditions

When an object moves down an inclined plane at a constant velocity, it implies that the net force along the plane is zero. This equilibrium means that the frictional force must exactly balance the component of gravitational force acting along the plane. Understanding this balance is key for determining the magnitude of friction and its role in modifying the net acceleration when the object’s motion changes.

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