Question

Two pulley arrangements $(A)$ and $(B)$ are as shown in the figure. Neglect the masses of the ropes and pulleys and the friction at the axle of the pulleys. The ratio of the acceleration of mass $m$ in arrangement $(A)$ to that in arrangement $(B)$ is

• A. $1:1$
• B. $1:2$
• C. $1:3$
• D. $2:1$

Answer 1

Answer: (C)

In case $A$, the acceleration of mass $m$ is
$a=\frac{(2m-m)g}{m+2m}=\frac{g}{3}$
In case $B$, the acceleration of mass $m$ is
$a^{\prime }=\frac{2mg-mg}{m}=g\therefore \frac{a}{a^{\prime }}=\frac{1}{3}$