Answer :

The acceleration of the mass M is


Given


The blocks are of “m” and “M” masses, with radius of r pulley and moment of Inertia “I”


Formula Used


The formula used to find the acceleration of the mass pulled/pushed is determined by the second law of Newton when the Force/Tension applied is equivalent to the product of mass and acceleration



where


is the force of the mass in terms of tension, is the acceleration and m is the mass of the block.


Explanation


The diagram 10.E4.1 is drawn below for better understanding of the kinematics of the blocks



The tension applied on the first block is



The tension applied on the block of mass “m” is



The torque applied on the pulley is derived as



The angular acceleration is changed into normal linear acceleration.





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