Physics : Motion of System of Particles and Rigid Bodies : Rolling Motion : Rolling on Inclined Plane

Solved Example Problems for Rolling on Inclined Plane(Rolling Motion)

### Example 5.23

Four round objects namely a ring, a disc, a hollow sphere and a solid sphere with same radius R start to roll down an incline at the same time. Find out which object will reach the bottom first.

*Solution*

For all the four objects namely the ring, disc, hollow sphere and solid sphere, the radii of gyration K are R, √(1/2) R, √(2/3) R, √(2/5) R (ref Table (5.3)). With numerical values the radius of gyration K are 1R, 0.707R, 0.816R, 0.632R respectively. The expression for time taken for rolling has the radius of gyration K in the numerator as per equation 5.63

The one with least value of radius of gyration K will take the shortest time to reach the bottom of the inclined plane. The order of objects reaching the bottom is first, solid sphere; second, disc; third, hollow sphere and last, ring.

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