Question

Two blocks are arranged as shown in the figure. What will be the relation between the accelerations $a_1$ of block $m_1$ and $a_2$ of block $m_2$, if the surface and the pulleys are frictionless and the strings are inextensible?

• A. $a_1$= $a_2$
• B. $a_1=6$$a_2$
• C. $a_1=3$$a_2$
• D. $a_1=4$$a_2$

Answer 1

The correct option is B $a_1=6$$a_2$

Since the strings are inextensible, therefore their length remains same. Let $a_A$ be the acceleration of the pulley A.
$\Rightarrow l_1+l_2=\text{constant}$
Double differentiating w.r.t time $t$, we get the equation in the form of acceleration i.e.
$\Rightarrow +a_A+(a_A-a_1)=0$
$\begin{array}{}\Rightarrow 2a_A=a_1& \text{(1)}\end{array}$
Also for the other string,
$l_3+l_4+l_5+l_6=\text{constant}$
Double differentiating w.r.t time $t$, we get the equation in the form of acceleration i.e.
$\Rightarrow -a_A+a_2+a_2+a_2=0$
$\begin{array}{}\Rightarrow a_A=3a_2& \text{(2)}\end{array}$
From $\left(1\right)$ and $\left(2\right)$, $a_1=6a_2$