Assume that the box and disk each have mass m, the top of the incline is at height h, and the angle between the incline and the ground is θ (i.e., the incline is at an angle θ above the horizontal). Also, let the radius of the disk be R. How much sooner does the box reach the bottom of the incline than the disk? Express your answer in terms of some or all of the variables m, h, θ, and R, as well as the acceleration due to gravity g.

Q: Question 13: A block of mass M is released at rest and it is under going a circular motion in a path…

A: given that  mass of block = M radius of path = R friction force f=bθ2/3

Q: PART D

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Central Force

Central force is the force that acts along the center of mass of one body to the center of mass of another body. Its direction from or away from a point on a body to another is called the center of the force. Such forces include gravitational force between two massive objects or electrostatic forces between two charged particles. So from atoms to planets, the central forces play an important role in shaping our daily lives. One of the remarkable features of central forces is that they are conservative, i.e. the total energy of a central force system can always be expressed as a gradient of a potential energy function.