For a hollow cylinder and a solid cylinder rolling without slipping on an inclined plane, then which of these reaches earlier

Question

For a hollow cylinder and a solid cylinder rolling without slipping on an inclined plane, then which of these reaches earlier (A) solid cylinder (B) hollow cylinder (C) both simultaneously (D) can't say anything

Tardigrade Admin · Accepted Answer

Solid sphere reaches the bottom first because for solid cylinder

\frac{K ^{2}}{R ^{2}} = \frac{1}{2},

and for hollow cylinder

\frac{K ^{2}}{R ^{2}} = 1

.
Acceleration down the inclined plane

\propto \frac{1}{K ^{2} / R ^{2}}

.
Solid cylinder has greater acceleration, so it reaches the bottom first.

Q. For a hollow cylinder and a solid cylinder rolling without slipping on an inclined plane, then which of these reaches earlier

solid cylinder

hollow cylinder

both simultaneously

can't say anything

Solid sphere reaches the bottom first because for solid cylinderR2K2​=21​, and for hollow cylinderR2K2​=1. Acceleration down the inclined plane ∝K2/R21​. Solid cylinder has greater acceleration, so it reaches the bottom first.