Question

Find the velocity of 'B' if the end of the rope is pulled with a speed of $1\text{m/s}$.
(Given that '$B$' is constrained to move along vertical)

• A. $\frac{1}{2}\text{m/s}$
• B. $\frac{1}{3}\text{m/s}$
• C. $\frac{3}{4}\text{m/s}$
• D. $\frac{3}{8}\text{m/s}$

Answer 1

The correct option is D $\frac{3}{8}\text{m/s}$

By length constraint if rope is moved by $1\text{m}$, pulley moves by $\frac{1}{2}\text{m}$.

$\therefore$ Velocity of $A$ is $\frac{1}{2}\text{m/s}$
By condition of wedge contraint the velocity along common normal remains same.
$V_B\cos \theta =V_A\sin \theta$
$V_B=V_A\tan \theta$
$=\frac{1}{2}\left(\frac{3}{4}\right)$
$=\frac{3}{8}\text{m/s}$