Answer to Question #115492 in Classical Mechanics for Suman

Question

If pulleys shown in the diagram are smooth and massless and A1 and A2 are acceleration of blocks of mass 4 kg and 8 kg respectively,then

Answer 1

This configuration of pulleys decreases the load for the hanging mass twice, that is, it seems like the mass of 4 kg is on the surface instead of 8 kg. But gain in force leads to decrease in displacement (or acceleration). Therefore, the acceleration of the 4 kg mass will be twice as higher than the acceleration of 8 kg mass:

$$a_1=2a_2.$$