Q. A system of three particles having masses $m_{1} = 1$ kg and $m_{3} = 4$ kg respectively is connected by two light springs. The acceleration of the three particles at any instant are $1ms^{- 2},2ms^{- 2}$ and 0.5 $ms^{- 2}$ respectively directed as shown in the figure. The net external force acting on the system is
A) 1 N
B) 7 N
C) 3 N
D) None of these
Explanation
(c) $\therefore\ \ {\overrightarrow{a}}_{CM} = \frac{{\overrightarrow{F}}_{eq}}{(m_{1} + m_{2} + m_{3})} = \frac{m_{1}{\overrightarrow{a}}_{1} + m_{2}{\overrightarrow{a}}_{2} + m_{3}{\overrightarrow{a}}_{3}}{(m_{1} + m_{2} + m_{3})}$
$\therefore{\overrightarrow{F}}_{eq} = m_{1}{\overrightarrow{a}}_{1} + m_{2}{\overrightarrow{a}}_{2} + m_{3}{\overrightarrow{a}}_{3}$
$= 1 \times 1 + 2 \times 2 + 4 \times ( - 0.5) = 1 + 4 - 2 = 3$ N
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.