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

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: 15

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<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/8dc73293b3f3aecf02934a255de0a338-.png" /> In case A, the acceleration of mass m is a=((2m-m)g/m+2m)=(g/3) In case B, the acceleration of mass m is a'=(2mg-mg/m)=g ∴ (a/a')=(1/3)

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

1 : 1

1 : 2

1 : 3

2 : 15

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
$a^{'} = \frac{2 m g - m g}{m} = g ∴ \frac{a}{a ^{'}} = \frac{1}{3}$

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

1 : 1

1 : 2

1 : 3

2 : 15

In case A, the acceleration of mass m is a=m+2m(2m−m)g​=3g​ In case B, the acceleration of mass m is a′=m2mg−mg​=g∴a′a​=31​

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
$a^{'} = \frac{2 m g - m g}{m} = g ∴ \frac{a}{a ^{'}} = \frac{1}{3}$