The pulley in the figure(Figure 1) represents different pulleys that are attache

Question

The pulley in the figure(Figure 1) represents different pulleys that are attached with outer radius and inner radius indicated in the table. The horizontal rope is pulled to the right at a constant linear speed that is the same in each case, and none of the two seperate ropes slips in its contact with the pulley. Part A Rank these scenarios on the basis of the linear speed of the block. Overlap this if equivalent

1.R outer=0.4m, R inner=0.2m

2.R outer= 0.8 m R inner = 0.4m

3.R outer =0.2 m R inner= 0.1m

4.R outer=0.6m R inner = 0.2m

5.R outer= 0.4m R inner = 0.3m

6.R outer= 0.6m R inner=0.5m

Explanation / Answer

If represents the angular speed of the pully , u represents the linear speed of the rope and v represent the upward velocity of the mass, then following relation holds

u = R * and v = r *

v = (r/R)* u

Thus the order depends on the ratio r / R

6 (0.83) , 5(0.75) , 4 (0.33) , 1, 2, 3 (all 0.5)

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