A sphere is given an initial push so that it starts rolling (without slipping) up an inclined plane. During its climb

Step-by-step solution

Let the upward direction along the inclined plane be positive. The sphere rolls up the incline, so its velocity v is positive and decreasing due to the component of gravity down the incline. For rolling without slipping, the relation between linear velocity and angular velocity is v = R . Since v is decreasing, the angular velocity must also decrease. To decrease the angular velocity, an angular deceleration is required in the direction opposite to the rotation. The forces acting on the sphere are gravity, normal r