Question

In the pulley system shown in figure the movable pulleys $A,B$ and $C$ are of mass $1\text{kg}$ each. $D$ and $E$ are fixed pulleys. The strings are light and inextensible. Choose the correct alternative(s). All pulleys are frictionless.

• A. Tension in the string is $6.5\text{N}$
• B. Acceleration of pulley $A$ is $g/3$ downward
• C. Acceleration of pulley $B$ is $g/6$ upward
• D. Acceleration of pulley $C$ is $g/3$ upward

Answer 1

Answer: (A), (B), (D)

The correct options are
A Tension in the string is $6.5\text{N}$
B Acceleration of pulley $A$ is $g/3$ downward
D Acceleration of pulley $C$ is $g/3$ upward

For finding the constraint realtion between blocks A, B and C, let's assume the acceleration of blocks are $a_A,a_B$ and $a_C$ and in downward direction.
Apply intercept method for $l_1,l_2,....l_6$ in diagram we get,
$a_c-a_B+a_c+a_A+a_A+a_B+a_B-a_A=0$
$a_A+a_B+2a_C=0$

Consider the FBD of different blocks and apply Newton's law seperately,
Let tension in string be $T$

$m_{A}g-T=m_A{a}_A,m_{B}g-T=m_B{a}_B,m_{C}g-2T=m_C{a}_C$
$\Rightarrow T=6.5\text{N},a_A=\frac{g}{3},a_B=\frac{g}{3},a_C=-\frac{g}{3}$