Question

Determine the speed with which block B rises up (as shown in the figure) if the end of the cord at A is pulled down with a speed of $2m/s$.

• A. 8 m/s
• B. 0.4 m/s
• C. 4 m/s
• D. 0.5 m/s

Answer 1

The correct option is D

0.5 m/s

Okay

Let's take ceiling as reference point

Marking position of pulley C, D and A

Assuming direction of velocity of C and E

There are two strings

Lets find their length

$(x_A-x_C)+(x_E-x_C)+x_E=l_1$

$\Rightarrow$ $x_A+2x_E-2x_C=l_1$

Differentiating with $t$ we get

$v_A-2v_E-2v_C=0$

$\because$ as string length is decreasing according to our assumed direction of velocity.

$v_A=2v_E+2v_C$ ....(1)

Now for the second string

$x_C+x_E=l_2$

differentiating

$v_C-v_E=0$

as $x_E$ is decreasing by our assumed direction of velocity

$v_C=v_E$ ....(ii)

substituting this in eg (i) we get

$v_A$ = $4v_E$

The velocity of block and pulley are same

$\Rightarrow$ $v_A$ = $4v_B$

$v_A$ = $2m/s$

$v_B$ = $0.5m/s$ in the upward direction.