Question

In the system shown in the figure, the acceleration of 1kg mass is :

• A. $\frac { \mathrm { g } } { 4 }$ downwards
• B. $\frac { \mathrm { g } } { 2 }$ downwards
• C. $\frac { \mathrm { g } } { 2 }$ upwards
• D. $\frac { \mathrm { g } } { 4 }$ upwards

Answer 1

Answer: (C)

$\frac { \mathrm { g } } { 2 }$ upwards

Answer 2

If a is downward acceleration of 4 kg block, the upward acceleration of 1 kg block must be 2a

Let T be tension in each part of string. The equation of motion on 4 kg block is

$4 g - 2 T = 4 a$ ….. (i)

The equation of motion or 1 kg block is

$T - 1 g = 1 \times 2 a$ …(ii)

Or $2 T - 2 g = 4 a$ ….(iii)

Adding (i) and (iii) we get

$2 g = 8 a$ or $a = \frac { g } { 4 }$

$\therefore$Acceleration of 1 kg block

$= 2 a = \frac { g } { 2 }$ upwards.