There are two marbles a and b of equal mass size and texture...

There are two marbles (A and B) of equal mass, size, and texture are racing down a sandy hill. Marble B has a hole drilled through it. When B rolls, the hole is parallel to the ground the whole time . Explain why marble B has an advantage.

Transcript

00:01 That i know from solid cylinder rolls without slipping down an incline but then a hole is drilled through the cylinder along its axis so the radius of the hole is 0 .5 times the outer radius of the cylinder so in question a i was asked does the cylinder take more or less time to roll down the incline now that the hole has been drilled so there's solve this so we assume so we assume this to be the incline of height age and here is the cylinder and this is the cylinder we assume and we assume it's radius to be r it's uniform cylinder so when it comes to at the bottom we assume the velocity is v so we should we'll find the velocity using the work energy theorem which is the potential energy equals to the kinetic energy at bottom plus the rotational energy the cylinder rolls without slipping so we can just write the moment of inertia of the cylinder is half m the mass into radius squared and we assume the cylinder is rolling without slipping so we can write omega v divided by r whole squared so by this we can just find v from here from here we just get v equals to v equals to root over 4 divided by three g gravitational constant a to h which is the height so the time it takes so the time it takes to go down we can find through this equation v equals to u plus 80 here is the acceleration we assume it to be constant so initial velocity is zero and the final velocity is root 3 by 4 to gh equals to 0 plus acceleration into time so the time taken t equals to sorry it is root over 4 by 3 root over 3 g to h divided by the acceleration so it is the time taken for the uniform cylinder so now we come to per second part that it is to toward the radius a hole is drilled along the axis of the cylinder and the radius of the hole is 0 .5 times of the outer radius.

03:50 So we again assume this to be the new cylinder.

04:03 So this is the inner radius and this is the outer radius...

Question

There are two marbles (A and B) of equal mass, size, and texture are racing down a sandy hill. Marble B has a hole drilled through it. When B rolls, the hole is parallel to the ground the whole time . Explain why marble B has an advantage.

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