You place three objects: a hoop, a disk and a solid sphere...

You place three objects: a hoop, a disk and a solid sphere next to each other at the top of an incline of height $h$ and release them from rest at the same instant. Assume: $I_{hoop} = MR^2$, $I_{disk} = frac{1}{2}MR^2$, $I_{sphere} = frac{2}{5}MR^2$ A. If they roll without slipping, what are the speeds of each when they reach the bottom? (Use any variable or symbol stated above along with the following as necessary: $g$ for the acceleration of gravity.) B. If they slide without rolling and without friction, what are the speeds of each when they reach the bottom?

Transcript

00:01 Hello student in this question the moment of inertia of the hoop disc and spare is given now we have to calculate the velocity in case of hope and the disk okay so first of all we know in the a part the final energy this will be equals to the initial energy okay this will be close to m g as multiple of initial this will be close to half m b square plus half i omega square of final right so solving this we get that m g this is equal to half m v square plus half i omega can be written as b divided by r square okay now if we are considering for the hoop okay we are considering the case for the hoop okay so half m b square plus half i will be mr squared multiplied by b b squared by r square and this will be equals to what m g x so from here the value half m b square plus this will be half m v square and this is equals to m gh so from here m v square will be equals to m gh and what is the value of b this is equal to root of g h so this is for the hoop okay now considering for the disk in case of the disk we are considering the case for the disk so what is this equals to half m v square plus half of half m r square multiplied by b squared divided by r square equals to m dh so it will cancel out and the value will be half m b square plus 1 divided by 4 b square n and this is equals to m g h so from here b will be equals to what 4 divided by 3 g h and its root okay for the case of the disk now we are considering for the sphere okay so for the sphere what is this equals to the velocity will be equals to what? so this is half mv square plus half multiplied by 2 divided by 5 m r square minus v squared divided by r square equals to m g h right so from here it is half m v square plus 1 divided by 5 mb square equals to m g h so from here 7 divided by 10 mv square will be m g h the velocity will be root of 10 divided by h d h so this is the velocity in all the three cases.

02:23 Now for the v part, we have to calculate the expression for the velocity again.

02:28 So if there are no sliding energy, there is no rotational energy...

Question

Please give Ace some feedback