A smooth inclined plane is fixed inside a car that is accelerating along a horizontal road, as shown in the figure. The car's acceleration a and the angle of the incline heta are related by the equation a = g . If a sphere is set into pure rolling on this incline,

Step-by-step solution

In the frame of the accelerating car, a pseudo force ma acts on the sphere in the horizontal direction opposite to the car's acceleration. The forces acting on the sphere along the inclined plane are the component of weight down the incline, mg , and the component of pseudo force up the incline, ma . The net force along the incline is: F_ net = mg - ma Substituting a = g into the equation gives: F_ net = mg - m(g ) F_ net = mg - mg = 0 Since the net force along the incline is zero, the linear acceleration of the sp