Shown in the figure is a system of three particles of mass 1 kg, 2 kg and 4 kg connected by two springs. The acceleration of A, B and C at any instant are 1 ms $^{- 2}$ , 2 ms $^{- 2}$ and 1/2 ms $^{- 2}$ respectively directed as shown in the figure external force acting on the system is

1 N

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7 N

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3 N

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none of these

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Solution

The correct option is C 3 N
External force acting on a body= $(m a s s o f t h e b o d y) \times (a c c . o f c e n t r e o f m a s s) = M \times a_{c m} a_{c m} = (m_{1} a_{1} + m_{2} a_{2} + m_{3} a_{3}) / (m_{1} + m_{2} + m_{3}) = (2 + 2 - 1) / 7 = 3 / 7 T h e r e f o r e F_{e x t} = 7 \times 3 / 7 = 3 N$

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