Two metal disks, one with radius r1 = 2.45 cm and mass m1 = 0.900 kg and the other with radius r2 = 5.00 cm and mass m2 = 1.60 kg, are welded together and mounted on a frictionless axis through their common center. a light string is wrapped around the edge of the smaller disk and a 1.60 kg block is suspended from the free end of the string. (a) what is the magnitude of the downward acceleration of the block after it is released? (b) repeat the calculation of part (a), this time with the string wrapped around the edge of the larger disk.

part (a)

Part (b)

Explanation:

Given,

Both the disks are welded together, therefore total moment of inertia of the both disks are the summation of the individual moment of inertia of the disks.

part (a)

Given that a block of mass m which is hanging with the smaller disk,

Let 'T' be 'a' be the tension in the string and acceleration of the block.

From the free body diagram of the smaller block,

From the pulley,

From the equation (1) and (2),

part (b)

Above expression for the acceleration of the block is only depended on the radius of the pulley.

Radius of the larger pulley =

Let be the acceleration of the block while connecting to the larger pulley.

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