Question

In the shown pulley system we have $m_2>m_1$. Neglecting the masses of the string and pulley and ignoring the friction in the system, we find that:

• A. Weights fall freely. Pulley $B$ rotates clockwise and pulley $A,C$ rotate anticlockwise
• B. The two weights have different accelerations. Pulley $C$ rotates clockwise and $B,C$ rotate anticlockwise
• C. Acceleration of masses will be zero and the system will be at rest
• D. Acceleration of masses is equal to $g$. Pulley $A$ and $C$ rotate clockwise whereas $B$ rotates anticlockwise.

Answer 1

The correct option is A Weights fall freely. Pulley $B$ rotates clockwise and pulley $A,C$ rotate anticlockwise

Here $m_{1}g-T=m_1{a}_1$($a_1$ is the downward acceleration of $m_1$).
and
$2T-m_{2}g=m_2{a}_2$($a_2$ is the upward acceleration of $m_2$).
As the mass of the pulley is zero we have $2T-T=0$ Thus $T=0$.
Thus we get $a_1=a_2=g$. thus the masses fall freely.
The motion of the pulley according the arrow sign as shown in figure. Pulley B will move clockwise and pulley A and C will move anti-clockwise. As the pullies are smooth, so the masses fall freely.
Ans:(A)