Question

please solve this it is urgent ​

Answer 1

Let the acceleration at point C be $\sf{a_C}$ in upward direction.

We consider downward motion as positive and upward motion, negative.

The point A is going with acceleration $\sf{a_A=2\ m\,s^{-2}}$ downwards.

The point B is going with acceleration $\sf{a_B=3\ m\,s^{-2}}$ downwards.

The top two pulleys are fixed, so the points of contact of these pulley with the string have no acceleration.

The two points of contact of the bottom pulley with the string goes with acceleration $\sf{a_B}$ downward.

So by constraint equation, since the string has no extension nor compression,

$\sf{\longrightarrow a_A+0+0+a_B+a_B+0+0-a_C=0}$

$\sf{\longrightarrow a_C=a_A+2a_B}$

$\sf{\longrightarrow a_C=2+2\times3}$

$\sf{\longrightarrow\underline{\underline{a_C=8\ m\,s^{-2}}}}$

I.e., the point C moves with acceleration $\sf{a_C=8\ m\,s^{-2}}$ upwards.