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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:

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10N

answer is C.

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Detailed Solution

The acceleration of centre of mass of the system

$a_{cm} = \frac{|m_{1} {\vec{a}}_{1} + m_{2} {\vec{a}}_{2} + m_{3} {\vec{a}}_{3}|}{m_{1} + m_{2} + m_{3}}$

$\Rightarrow$ The net force acting on the system

$= |m_{1} {\vec{a}}_{1} + m_{2} {\vec{a}}_{2} + m_{3} {\vec{a}}_{3}|$

$\begin{array}{l} \Rightarrow F_{net} = (m_{1} a_{1} + m_{2} a_{2} - m_{3} a_{3}) \\ \Rightarrow F_{net} = [(1) (1) + (2) (2) - \frac{1}{2} (4)] N = 3 N \end{array}$

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