The correct answer is D (1.4m/s), but can someone show me how to get the answer?

Question

The correct answer is D (1.4m/s), but can someone show me how to get the answer?

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QUESTION 6** This and the nay three questions refer to this situation: Two masses. m1 = 3 kg and m2 = 2 kg. are suspended with a massless rope over a pulley of mass 31 = 10 kg. The pulley turns without friction and may be modeled as a uniform disk of radius R = 0.1 m. You may neglect the size of the masses. The rope does not slip on the pulley. The system begins at rest. If mi starts at a height h = 1 m above the ground, what is its speed v when it hits the ground? (a) v = 3.82 m/s (b) v = 2.97 m/s (c) v = 2.04 m/s (d) v = 1.40 m/s (e) v = 0.981 m/s

Explanation / Answer

Let it reach the ground with velocity v.

Change in KE of m1, KE1=0.5*3*v2=1.5v2

Change in KE of m2, KE2=0.5*2v2=v2

Decrease in PE of m1=mgh=3*9.8*1=29.4

Increase in PE of m2=2*9.8*1=19.6

Change in KE of pulley=0.5Iv2/R2=(0.5*10*0.12)*v2/0.12=2.5v2

Now, from law of conservation of energy,

29.4=19.6+1.5v2+v2+2.5v2

5v2=9.8

v=1.4 m/s

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