Question

Consider two solid uniform cylinders that have the same mass and length, but different radii: the radius of cylinder A is much smaller than the radius of cylinder B. Rolling down the same incline, which one of the two cylinders will reach the bottom first? Assume both cylinders are rolling without slipping (pure roll).
a) cylinder A
b)cylinder B
c)both in same time.

Answer 1

I=mr²/2
mgh= mv²/2 +Iω²/2 =
=mv²/2 +mr²v²/r²4 =
= mv²/2+ mv²/4
=3mv²/4
v=sqrt{4gh/3} =>
c)both in same time.