Question

In $Fig$, man A is standing on a movable plank while man b is standing on a stationary platform. Both are pulling the string down such that the plank moves slowly up. As a result of this the string slips through the hands of the men. Find the ratio of length of the string that slips through the hands of A and B.

• A. $3/2$
• B. $3/4$
• C. $4/3$
• D. $2/3$

Answer 1

The correct option is C $4/3$

R.E.F image

$\bullet$ The length of the string passing over pulley $2=L_1+L_2$

$\bullet$ If plank moves up by $x_1,$ then pulley 2 moves down by $x_1$

$\bullet$ Let the length of string that slips through B be $x_2$

$\bullet$ Then after displacement, length of the string passing

over pulley $2=L_1-2x_1+L_2+x_2-x_1=L_1+L_2-3x_1+x_2$

$\bullet$ Since inital length of string = final length of string

$L_1+L_2=L_1+L_2-3x_1+x_2\Rightarrow x_2=3x_1$

$\therefore$ length of string that slips through $A=x_2+x_1=4x_1$

and length of string that slips through $B=x_2=3x_1$

$\therefore$ The ratio of length of string that slips through

the hands of A and B is $\frac{4x_1}{3x_1}=\frac{4}{3}$