Consider the situation shown in the given figure. The light smooth pulley C is movable, but the smooth
pulley D is fixed. The ratio of speeds of block A and B, when block A moves a distance 2m is Va/Vb .Find nth value of Va/Vb
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Explanation:
Since, all strings are connected to each other, it will have some tension at all point, let it be T.
Considering the acceleration of pulley, A,B and C is a1,a2 and a3 downward.
→ according to constrain equation,
∑T.a=0
−2Ta3−T.a2−Ta1=0
2a3+a2+a1=0→(1)
Applying Newton''s laws on each block,
10−2T=a3→(2)
10−T=a2→(3)
10−T=a1→(4)
From equation (2) and (3)
−T=a3−a2
T=a2−a3→(5)
putting it in
10−a2+a3=a2
2a2=10+a3→(6)
Solving (2) and (4), we get,
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