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 slops through the hands of the men, find the ratio of length of the string that slips through the hands of A and B.

Options

A. `3//2`
B. `3//4`
C. `4//3`
D. `2//3`

Answer

C

Explanation

Let the plank move up by x, then pulley 2 will move down by x. Let the end of string C moves down by a distance y.
Let the initial length of string passing over pulley 2,
`l_(1)+l_(2)`…(i)
After displacements x and y mentioned above, the lengths become
`(l_(1)-2x)+(l_(2)+y-x)` ..(ii)
Equating Eqs. (i) and (ii), we get `y=3x`
Length of string that slips through A is `y+x=4x` and through B is `y=3x`.
Required ratio=`(4x)/(3x)=4/3`