Question

In the figure shown, the acceleration of A is $2m/s^2$ to left and acceleration of B is 1 $m/s^2$ to left.

Find the magnitude of acceleration of C in $m/s^2$

• A. 1 $m/s^2$ upwards
• B. 1 $m/s^2$ downwards
• C. 3 $m/s^2$ upwards
• D. 3 $m/s^2$ downwards

Answer 1

The correct option is A

1 $m/s^2$ upwards

Its only one single string
Take pulley P as reference. Mark positions of A, B, C with respect to P.
Now assume acceleration of C as up, differentiating

$l=2x_A+2x_B+2x_C$
$\frac{dl}{dt}=0\therefore l$ is constant
$0=2v_A-2v_B-2v_C$

$\frac{d{x}_A}{dt}=+v_A\therefore$ Acceleration is increasing it
$\frac{d{x}_B}{dt}=-v_B\&\frac{d{x}_C}{dt}=-v_C$
$\Rightarrow v_B+v_C=v_A$
$\Rightarrow a_B+a_C=a_A$
$\Rightarrow 1+a_C=2$
aC = 1 $m/s^2$ upwards as we assumed it
If you would have assumed $a_C$ downwards in the beginning then you would have got $a_C$ = -1 which means your assumption is wrong its going in opposite direction.