Question

Find the acceleration of block $A$ if block $C$ is moving with acceleration $a=3{\text{m/s}}^2$ as shown in the figure. Assume the surface to be frictionless and pulleys and string ideal. Take $g=10m/s^2$

• A. $2m/s^2$
• B. $1m/s^2$
• C. $4m/s^2$
• D. $5m/s^2$

Answer 1

The correct option is B $1m/s^2$

The given system can be reframed as shown

From constraint condition and using method of intercept we have,

${\stackrel{..}{L}}_1+{\stackrel{..}{L}}_2+{\stackrel{..}{L}}_3+{\stackrel{..}{L}}_4=0$
$\Rightarrow -a_A-a_B-a_B+a=0$
$\Rightarrow 2a_B=a-a_A\dots \dots \left(1\right)$

From FBD of $A$ and $B$
$T-5g=5a_A\dots \dots \left(2\right)$
$2T-10\text{g}=10a_B\dots \dots \left(3\right)$
On solving above two equation, we get
$a_A=a_B$
Putting this value in equation $\left(1\right)$, we get
$3a_A=a=3{\text{m/s}}^2$
$\Rightarrow a_A=1{\text{m/s}}^2$
Hence, acceleration of block $A$ is $1{\text{m/s}}^2$