A uniform spherical shell of mass M = 7.90 kg and radius R = 0.880 m can rotate

Question

A uniform spherical shell of mass M = 7.90 kg and radius R = 0.880 m can rotate about a vertical axis on frictionless bearings (see the figure). A massless cord passes around the equator of the shell, over a pulley of rotational inertia I = 0.150 kg

A uniform spherical shell of mass M = 7.90 kg and radius R = 0.880 m can rotate about a vertical axis on frictionless bearings (see the figure). A massless cord passes around the equator of the shell, over a pulley of rotational inertia I = 0.150 kg·m2 and radius r = 0.120 m, and is attached to a small object of mass m = 4.60 kg. There is no friction on the pulley's axle; the cord does not slip on the pulley. What is the speed of the object when it has fallen a distance 0.677 m after being released from rest? Use energy considerations.

Explanation / Answer

from energy conservation we get,

rotational energy of sphere + rotational energy of pulley + K.E of the mass = mgh

so, 1/2*(2/3 mr^2)w1^2 + 1/2*(I given)*w2^2 + 1/2*m*(v)^2 = m*g*h

w1 = v/.88

w2 = v/.12

calculating we get v = 1.7461 m/s

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