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A hollow sphere rolls down at 30 degree incline of length 6M without slipping the speed of centre of mass of the bottom of the plane is

A hollow sphere rolls down at 30 degree incline of length 6M without slipping the speed of centre of mass of the bottom of the plane is

Grade:11

1 Answers

Agrata Singh
208 Points
5 years ago
Since the sphere rolls down without slipping, it is performing pure rolling motion
Hence v=Rw
Applying conservation of energy (Let the mass of sphere be m)
 
Ei=mgh(h=6sin30 the height of top of incline from ground)
Ei=m10(6sin30)
Ei=30m
 
Ef=1/2mv2+ 1/2Iw2  ( I is the moment of inertia I=2/3 MR2 for hollow sphere) 
Ef=1/2mR2w2+ 1/2(2/3mR2)w2
Ef=5/6mR2w2
 
Solving  Ei=Ef you will have 
R2w2=36
Rw=6=vcm
 
Hope this helps
 

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