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A souvenir is constructed by 3 light rods, light strings and four objects as shown. If the system is in equilibrium, if mass $m_{3}$ is $(81 + x) gm$ , then the value of x is $____$ .

Original source figure, Advanced Section-II(ii) Q8

Answer:

3

Solution:

Balance torques on the lowest rod.

$(12) (3) g = m_{1} (4) g$

$m_{1} = 9 g$

Balance torques on the middle rod.

$m_{2} (2) g = (12 + 9) (4) g$

$m_{2} = 42 g$

Balance torques on the top rod.

$m_{3} (3) g = (42 + 12 + 9) (4) g$

$m_{3} = 84 g$

$81 + x = 84$

$x = 3$

Stream:JEESubject:PhysicsTopic:NLMSubtopic:FBD & Equilibrium

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