A solid sphere,a ring , and a disc all having same radius and same mass are made to roll on an inclined plane which one of them reaches fastest on ground

A solid sphere,a ring , and a disc all having same radius and same mas

1.	A solid sphere,a ring , and a disc all having same radius and same mass are made to roll on an inclined plane which one of them reaches fastest on ground
Answer» Assume each object has the same mass and the same outside diameter. ΣTA=IAα I will assume clockwise ROTATION = positive, ∴mg(sinθ)R=(IA)α but α=aR ∴mg(sinθ)R=(IA)aR or a=mg(sinθ)R2IA but the PARALLEL axis theorm states IA=IC+mR2 a=mg(sinθ)R2IC+mR2 The object with the smallest mass moment of inertia (IC) will have the largest ACCELERATION down the plane. Solid Sphere: IC=25mR2 Solid CYLINDER: IC=12mR2 Thin walled Hollow Sphere: IC=23mR2 The solid sphere wins the RACE

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A solid sphere,a ring , and a disc all having same radius and same mass are made to roll on an inclined plane which one of them reaches fastest on ground

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