Question

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

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

Answer 1

Answer: (C)

If $a$ is downward acceleration of $4kg$ block, the upward acceleration of $1kg$ block must be $2a$.
Let $T$ be tension in each part of string.
The equation of motion on $4kg$ block is
$4g-2T=4a$ $...\left(i\right)$
The equation of motion on $1kg$ block is
$T-1g$ $=1\times 2a$ $...\left(ii\right)$
or $2T$$-2g$ $=4a$ $\dots \left(iii\right)$

Adding (i) and (iii), we get
$2g$$=8a$ or $a=\frac{g}{4}$
$\therefore$ Acceleration of $1kg$ block $=2a$ $=\frac{g}{2}$ upwards.