Question

Velocity of block B in the given arrangement is $300mm/sec$ towards right. Then velocity of A will be

• A. $200mm/sec$
• B. $100mm/sec$
• C. $450mm/sec$
• D. $150mm/sec$

Answer 1

The correct option is A $200mm/sec$


Assume rightward direction to be +ve
For pulley 1,
$v_1=v_B=\frac{v_C+v_D}{2}$
$v_C=0$ since that end of the string is fixed.
$\Rightarrow v_D=2v_B--\left(1\right)$

For pulley 2,
$v_2=v_A=\frac{v_E+v_F}{2}$
$v_E=v_D$
$\Rightarrow v_A=\frac{2v_B+v_F}{2}--\left(2\right)$ (using (1))

Pulley 3 is fixed
$\Rightarrow v_G=v_H=v_A$
But $v_F=v_G$
$\therefore v_F=-v_A--\left(3\right)$
(because direction is opposite to that of A)

Substituting (3) in (2),
$v_A=\frac{2v_B-v_A}{2}$
$\Rightarrow 3v_A=2v_B$
$\Rightarrow v_A=\frac{2v_B}{3}=\frac{2\times 300mm/sec}{3}$
$\Rightarrow v_A=200mm/sec$