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a solid sphere of mass M and radius r rolls inside hemispherical bowl of radius R without slipping from the rim of a hemispherical cup so that it rolls along the surface. If the rim of the hemisphere is kept horizontal .normal reaction exerted by the bowl on the sphere at the bottom point of the hemisphere is[ please provide required steps]

a solid sphere of mass M and radius r rolls inside hemispherical bowl of radius R  without slipping from the rim of a hemispherical cup so that it rolls along the surface. If the rim of the hemisphere is kept horizontal.normal reaction exerted by the bowl on the sphere at the bottom point of the hemisphere is[ please provide required steps]

Grade:11

2 Answers

Arun
25750 Points
3 years ago
 
According to Energy Conservation:-
mgR=1/2 (I of disc)(omega)² + 1/2 mv²
mgR=1/2 (mR²/2)(v/R)² + 1/2mv²
2mgR= 3/2 mv²
4/3 mg = v²/R
4/3 mg = a
 
Let Normal force be N
N - mg = ma
N - mg = 4/3 mg
N = 4/3 mg + mg
N = 7/3 mg
Vikas TU
14149 Points
3 years ago
Dear student 
Total normal force =mg+mv^2/R−r
Ag∈,mg(R−r)=1/2Iω2 + 1/2mv2
mg(R−r)=1/2x2/5mv^2+1/2mv^2
Good Luck 
Cheers 

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