Question

Shown in the figure is a system of three particles having masses m₁ =1kg, m₂ = 2kg and m₃ = 4 kg respectively connected by two springs. The acceleration of A, B and C at any instant are 1m/sec², 2m/sec² and 1/2 m/sec² respectively directed as shown in the figure. The external force acting on the system is

• A. 1N rightward
• B. 3N leftward
• C. 3N rightward
• D. Zero

Answer 1

Answer: (C)

3N rightward

Answer 2

The acceleration of center of mass of the system = ${\overrightarrow{a}}_{cm}$

= $\frac{\left| m_{1}{\overrightarrow{a}}_{1} + m_{2}{\overrightarrow{a}}_{2} + m_{3}{\overrightarrow{a}}_{3} \right|}{m_{1} + m_{2} + m_{3}}$⇒ The net force acting on the system = $(m_{1} + {\overrightarrow{m}}_{2} + m_{3}){\bar{a}}_{cm}$

⇒ F_net = (m₁ a₁ + m₂ a₂ – m₃ a₃)

= $\left\lbrack (1)(1) + (2)(2) - \frac{1}{2}(4) \right\rbrack$N= 3N.

Hence, the correct choice is