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
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