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Find acceleration of mass 1kg, 2kg and 3kg as shown in the attachment... .

Find acceleration of mass 1kg, 2kg and 3kg as shown in the attachment... .

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Grade:12th pass

1 Answers

Piyush Kumar Maurya
65 Points
5 years ago
 
Let the tension in the string connecting 1kg be T2 and T1 be the acceleration in the string string cog 2kg and 3kg block..
P1 be the pulley attached to the surface above and P2 be the pulley from which 2kg and 3kg block are hung.
So tension in the string between the two pulleys will be sum of tension from either of the string connecting 2kg and 3kg or the one connecting 1kg.
So.    T1+T1 =2T1 (considering the tension from      string connecting 2kg and 3kg block)
T2+T2 = 2T2 ( considering tension from string connecting 1kg block and the fixed point)
So 2T1 = 2T2 [ both are tension for same string between pulleys]
Therefore T1 = T2 
Let 'a' be the acceleration of 1 kg block. SoSo acceleration of Pulley 1 is equal to a/2. Similarly the acceleration of pulley 2 is equal to a/ 2.
Let ''ar' be the relative acceleration of 2 kg and 3kg . So acceleration of block 2kg will be, a2 = ar - a/2
And acceleration of block 3 kg will be, a3 = ar + a/2
blockswith respect to Pulley 2.
 For 1kg block      T2 = 1*a .      -----   (i) 
For 2kg block .     T1 - 20 = 2( ar  - a/2) .      ----(ii)
For 3 kg block      30 -T1 = 3 ( ar + a/2).      ----(iii)
On solving these equations we get 
T1 = T2 = 120/11N
a = 120/11 m/s^2
a2 = 50/11 m/s^2 downwards
a3 = 70/11 m/s^2 downwards

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