Question

Shown in the figure is a system of three particles having masses $\mathrm { m } _ { 1 } = 1 \mathrm {~kg}$, $\mathrm { m } _ { 2 } = 2 \mathrm {~kg}$ and $\mathrm { m } _ { 3 } = 4 \mathrm {~kg}$ respectively connected by two springs. The acceleration of A, B and C at any instant are $1 \mathrm {~m} / \mathrm { sec } ^ { 2 }$ , $2 \mathrm {~m} / \mathrm { sec } ^ { 2 }$ and $\frac { 1 } { 2 } \mathrm {~m} / \mathrm { sec } ^ { 2 }$ 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 centre of mass of the system

= $\overline { \mathrm { a } } _ { \mathrm { cm } } = \frac { \left| \mathrm { m } _ { 1 } \overline { \mathrm { a } } _ { 1 } + \mathrm { m } _ { 2 } \overline { \mathrm { a } } _ { 2 } + \mathrm { m } _ { 3 } \overline { \mathrm { a } } _ { 3 } \right| } { \mathrm { m } _ { 1 } + \mathrm { m } _ { 2 } + \mathrm { m } _ { 3 } }$

⇒ The net force acting on the system

= $\left( \mathrm { m } _ { 1 } + \overline { \mathrm { m } } _ { 2 } + \mathrm { m } _ { 3 } \right) \overline { \mathrm { a } } _ { \mathrm { cm } }$

⇒ $\mathrm { F } _ { \text {net } } = \left( \mathrm { m } _ { 1 } \mathrm { a } _ { 1 } + \mathrm { m } _ { 2 } \mathrm { a } _ { 2 } - \mathrm { m } _ { 3 } \mathrm { a } _ { 3 } \right)$

= $\left[ ( 1 ) ( 1 ) + ( 2 ) ( 2 ) - \frac { 1 } { 2 } ( 4 ) \right] \mathrm { N } = 3 \mathrm {~N}$