Question

State whether the given statement is True or False :

The velocity ratio of a combination of $n$ movable pulleys with a fixed pulley will be $2^n$.

• A. True
• B. False

Answer 1

The correct option is A True

Consider case of combination of three movable pulley and one fixed pulley:

Since the length of rope is always constant, writing constraint equation for single movable pulley $x_1+x_2+x_3=c$...(i) differentiating equation (i) $\frac{d}{dx}(x_1+x_2+x_3)=0$

from geometry $x_1=x_2$...(ii) substituting (ii) in equation (i)

$\frac{d}{dx}(2x_1+x_3)=0$...(iii) $\Rightarrow v_C=v_{effortend}/2$ velocity ratio $v_{effortend}/v_C=2$...(iv)

where $v_A,v_B,v_C$ denotes respective pulleys velocities

similarly $v_B=\frac{v_C}{2}$...(v)

and $v_A=\frac{v_B}{2}$...(vi)

combining equation (vi), (v) and (vi)

$v_A=\frac{v_{effortend}}{8}=v_A=\frac{v_{effortend}}{2^3}$

thus it can be generalised that for combination of 1 fixed pulleys and n movable pulleys the velocity ratio will be $2^n$