Question

w with doma as a light plastic outer la n d det somewhere in between the dentin of the materials used in incline that makes an angle with the vertical, a show is a form olid pler the threesphere hollow dense core uniform intermediate density a) (6 points) Rank the moments of inertin of the threesphere from get to smallest. Clearly indicate if any of the moments of inertiarena enotation like I -Ip. This is just An example to illustrate the notation, not a catteet a wer!) Explain your reasoning ) (6 points) All three spheres start from rest at the top of the same incline, with angle 8 from the vertical as shown, and roll down without slipping. Which reaches the bottom first? Prove your answer in energy ideas (7 points) In terms of the given symbols ( M R ) and any constants of nature you need, find an expression for the magnitude of the frictional force acting on sphere Cas it rolls down the inclme. Show your work

need 1a 1b and 1c

Answer 1

and we kno In > Ic 7 If because in case A mass is distributed farthest from centes that moment of inertia is equal to MR² if R is large than moment of inertia is large In case B mass is distributed nearest to the center horse it has least moment of inertia 602 Apply energy conservation Mg H = 2 mw2 + ² I w2 MgH = £mvh + ŽIVAL mgH = 2m + 2 7 ) Mot I 2RL from this relation we can see that Is has least value hence it have maximum velocity then therefore it reach to bottom first (B will reach first)

c) from fibido 1. d= MM and y = mg cose hence 18= Ming cosa In case & slipping When it is in pure rolling motion friction fource will be zero (f=o) because there is no relative motion at than point of contact