Question

Example 7.16 Three bodies, a ring, a solid
cylinder and a solid sphere roll down the
same inclined plane without slipping. They
start from rest. The radii of the bodies are
identical. Which of the bodies reaches this
ground with maximum velocity?​

Answer 1

Answer:

solid sphere

because.........

Explanation:

According to conservation of mechanical energy

or mgh=12mv2(1+k2R2)

v2=2gh1+k2R2

It is independent of the mass of the rolling body.

For a ring, k2=R2

vr∈g=2gh1+1−−−−−√=gh−−√

For a solid cylinder, k2=R22

vcyl∈der=2gh1+12−−−−−√=4gh3−−−−√

For a solid sphere, k2=25R2

vsphere=2gh1+25−−−−−√=10gh7−−−−−√

Among the given three bodies the solid sphere has the greatest and the ring has the least velocity at the bottom of the inclined plane

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