Two identical disks of mass M, radius R rotate about fixed axes of radius r with

Question

Two identical disks of mass M, radius R rotate about fixed axes of radius r with negligible mass. Identical masses, m, are attached to strings wrapped around the axis and the outer rim as shown in the figure. The masses are then released from rest at the same height h above the ground. Which one takes longer to hit the ground, and which mass m, has more kinetic energy when it hits the ground? The mass in I hits the ground first and has more kinetic energy. The mass in I hits the ground first. The mass in II has more kinetic energy. The mass in II hits the ground first and has more kinetic energy. The mass in II hits the ground first. The mass in I has more kinetic energy. Both masses reach the ground at the same time and have the same kinetic energy.

Explanation / Answer

The right answer is option C.

Bo the the huge discs have same moment of inertia. Torque is directly proportonal to the magnitude of the normal distance from axis to the point where force is acting. In figure 2 the distance from the axis to the point where the force due to the hung mass is acting is more. So there is more torque in 2.

  Now torque is directly proportonal to the angular accelaration of an object. Since 2 is experiencing more torque it should have more angular accelaration.

Since both the discs are starting from rest the one with greater angular accelaration rotates faster than the one with lesser angular accelaration. So 2 rotates faster.

The mass wich is attached to the faster rotating disc will touch the ground first and the it will have more velocity (or more kinetic energy).

Thank you for your support.

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