when a sphere,a ring ,disc and a spherical shell are coming down an inclined plane rolling without slipping,which will reach the ground first?PLEASE,do not give links.

Dear student,
Find the answer to your query as under:



Suppose that the mass of all the four objects is equal and the radius is different for each, and the height of the inclined plane is 'h'. Then
Now, 

PE = KEtranslational + KErotaional

FOR RING:

mgh = 0.5 mv2 + 0.5 Iω2
mgh = 0.5 mv2 + 0.5 mr2 × (m/r)2
mgh = 0.5 mv2  + 0.5 mv2
v = √gh

similarly, 
DISC:

mgh = 0.5 mv 2 + 0.25 mv2
or, 
v = √(1.33gh)

FOR Sphere:

v = √(1.42gh)

For Shell:
v = √(1.2gh)

Since, 
vsphere  is max thus, it is the sphere that rolls down the fastest and hence the first.



Regards
Satyendra Singh

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