A small block of mass ‘m’ is rigidly attached at point P to a ring of mass ‘3m’ and radius ‘r’. System is released from rest when radius vector makes an angle of 900 with the vertical (as shown) and rolls without sliding. Angular acceleration just after its release is g/pr, where p = _____ (g is acceleration due to gravity)

(mg−f)r=(3mr2+mr2)α……(1)f =4ma --- (2)Solving α=g8r

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A small block of mass ‘m’ is rigidly attached at point P to a ring of mass ‘3m’ and radius ‘r’. System is released from rest when radius vector makes an angle of 90⁰ with the vertical (as shown) and rolls without sliding. Angular acceleration just after its release is g/pr, where p = _____ (g is acceleration due to gravity)

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Detailed Solution

$(m g - f) r = (3 m r^{2} + m r^{2}) α$ ……(1)

f =4ma --- (2)

Solving $α = \frac{g}{8 r}$

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