Question

For the masses and ideal-massless pulleys shown in figure find the ratio of magnitudes of accelerations of masses $A$ and $B$. Pulley $C$ is fixed to the ceiling and pulley $D$ is free to move vertically. All strings are inextensible and assume the string length to be equal between the pulley D and C and between the pulley D and the rigid support.

• A. $0.5$
• B. $5$
• C. $2$
• D. $0.2$

Answer 1

The correct option is A $0.5$


Since the string is inextensible,
Length of string = constant
Let $x_A$ and $x_B$ be the intercepts of the string, then
$x_A+x_A+x_B=C$
$\Rightarrow 2x_A+x_B=C$
Differentiating w.r.t time, we get
$\Rightarrow |2V_A|+|V_B|=0$
Again differentiating w.r.t time, we get
$\Rightarrow |2a_A|+|a_B|=0$
$\Rightarrow |a_B|=2|a_A|$
$\left|\frac{a_A}{a_B}\right|=\frac{1}{2}=0.5$