1. Tardigrade
  2. Question
  3. Physics
  4. 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

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Q. 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

Laws of Motion

Solution:

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