A uniform spherical shell of mass M-11.0 kg and radius R 0.550 m can rotate abou

Question

A uniform spherical shell of mass M-11.0 kg and radius R 0.550 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 1 = 0.170 kg-m2 and radius r = 0.0900 m, and is attached to a small object of mass m = 2.20 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 0.960 m after being released from rest? Use energy considerations. M, R Number Units

Explanation / Answer

here,

M = 11 kg

R = 0.55 m

the accelration of object , a = net force /effective mass

a = ( m * g)/( m + I/r^2 + 2/3 * M * R^2 /R^2)

a = ( 2.2 * 9.81) /( 2.2 + 0.17/0.09^2 + 0.67 * 11)

a = 0.71 m/s^2

the speed of object , v = sqrt(2 * a * h)

v = sqrt(2 * 0.71 * 0.96) m/s

v = 1.17 m/s

the final speed is 1.17 m/s

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