Answer :

The acceleration of the mass if 1 kg 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-E7.1 as drawn below shows the tension horizontal as T’ and tension pulling the pulley as T which gives us the diagram as



The tension in terms of acceleration due to horizontal tension is




The angular acceleration of the pulley is given as



Hence, the torque applied by the pulley due to the mass is given as






Now finding the moment of Inertia we get the value of the mass M as




Putting the value of mass in tension equation, we get the equation of acceleration in terms of tension as



Again, putting the value of , we get





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