Question

In the figure acceleration of $A$ is $1 \,m/s^{2}$ upwards, acceleration of $B$ is $7 \,m/s^{2}$ upwards and acceleration of $C$ is $2 \,m/s^{2}$ upwards. The acceleration of D will be

• A. $7 \,m/s^{2}$ downwards
• B. $2 \,m/s^{2}$ downwards
• C. $10 \,m/s^{2}$ downwards
• D. $8\, m/s^{2}$ downwards

Answer 1

Answer: (C)

Acceleration of pulley $P$
$a_{p}=\frac{a_{A}+a_{B}}{2}$
$=\frac{1+7}{2}$
$=4\,m/s^{2}$ (upward)
Acceleration pulley Q will be $4\, m/s^{2}$ downwards

$a_{Q}=\frac{a_{D} - a_{c}}{2}$
$4=\frac{a_{D}-2}{2}$
$\Rightarrow a_{D}=10\,m/s^{2} (↓)$