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Question

In the arrangement shown in the figure, mA=2kg and mB=1kg. String is light and inextensible. Find the acceleration of centre of mass of both the blocks :
Neglect friction everywhere.

133345_bf9a7419b8df42deac8d032c0d53c748.jpg
  1. g/3 downwards
  2. g/9 downwards
  3. g/9 upwards
  4. g/3 upwards

A
g/3 downwards
B
g/9 upwards
C
g/9 downwards
D
g/3 upwards
Solution
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As mA>mB so acceleration of A is downward and B is upward. For downward assume acceleration is positive and for upward acceleration negative. i.e, aA=a and aB=a
Here, (mA+mB)a=(mAmB)g

(2+1)a=(21)ga=g3

thus, acm=mAaA+mBaBma+mB=2(g/3)+1(g/3)2+1=g/9 downward. (as it is positive)

226311_133345_ans_9a4d7418cd154754b29237fae106e720.png

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133345_bf9a7419b8df42deac8d032c0d53c748.jpg
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