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  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 <img class=img-fluid question-image alt=image src=https://cdn.tardigrade.in/img/question/physics/8b92ef27a920836d170c53c2992b008d-.png />

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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
image

Laws of Motion

Solution:

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