Question

The velocity of block B is x m/s. Then x is : (Pulley $P_1,P_2$ and $P_3$ are movable. All other pulleys are fixed).

• A. $20$
  
• B. $30$
  
• C. $32$
  
• D. $25$
  

Answer 1

The correct option is A $20$

Consider a body X at the end of the pulley moving with $2m/s$
Now,
making FBD of each body we have,
$v_B\Rightarrow$unknown
$v_A=10\uparrow$
$v_C=4\downarrow$
$v_X=2\downarrow$
Now the total work done due to tension force should be zero
$\therefore -T{a}_B+4T{a}_A-4T{a}_C-2T{a}_X=0$
$\therefore -T{v}_B+4T{v}_A-4T{v}_C-2T{v}_X=0$
$\therefore -a_B+4\left(10\right)-4\left(4\right)-2\left(2\right)=0$
$\therefore a_B=20\downarrow$