Question

If acceleration of block $A$ is $2{\text{m/s}}^2$ to left and acceleration of block $B$ is $1{\text{m/s}}^2$ to left, then what will be the acceleration of block $C$? Assume that the surface and pulleys are smooth and string is inextensible.

• A. $1{\text{m/s}}^2$ upwards
• B. $1{\text{m/s}}^2$ downwards
• C. $2{\text{m/s}}^2$ downwards
• D. $2{\text{m/s}}^2$ upwards

Answer 1

The correct option is A $1{\text{m/s}}^2$ upwards

Let the acceleration of the block C be $a_C$ and the acceleration for the intercepts of the string whose length is decreasing to be negative.
Since the string is inextensible,
$l_1+l_2+l_3+l_4+l_5=\text{constant}$
Double differentiating the above equation w.r.t time, we get the equation in the form of acceleration i.e.
$-a_c+2+2-1-1-a_c=0$
$a_c=1{\text{m/s}}^2\uparrow$