A small solid marble of mass and radius rolls down along the loop track, without slipping. Find the height above the base, from where it has to start rolling down the incline such that the sphere just complete the vertical circular loop of radius
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A solid ball of mass m and radius r rolls without slipping througha loop of radius R, as shown in the figure. From what height hshould the ball be launched in order to make it through the loopwithout falling off the track? (Use any variable or symbol statedabove along with the following as necessary: g.)
Hint:
A solid sphere and a hollow cylinder of the same mass and radius have a rolling race down an incline. They start at rest on an incline at a height h above a horizontal plane. The race then continues along the horizontal plane. The coefficient of rolling friction between each rolling object and the surface is the same. Which object rolls the farthest? (Justify your answer with an algebraic expression.)
