Question

Assuming that the string is inextensible and pulleys are smooth and light for the arrangement shown in the figure, choose the correct option(s).

• A. Acceleration of $1kg$ block is $\frac{g}{3}$ upward.
• B. Acceleration of $1kg$ block is $\frac{g}{3}$ downward.
• C. Acceleration of $2kg$ block is $\frac{2g}{3}$ upward.
• D. Acceleration of $2kg$ block is $\frac{2g}{3}$ downward.

Answer 1

Answer: (A), (D)

The correct options are
A Acceleration of $1kg$ block is $\frac{g}{3}$ upward.
D Acceleration of $2kg$ block is $\frac{2g}{3}$ downward.

Let he acceleration of block of mass $1kg$ and $2kg$ be $a_1$ and $a_2$ respectively.
From the intercept concept the given arrangement is shown as

$l_1+l_2+l_3=\text{constant}$
Double differentiating the above equation, we get
$\stackrel{.}{l_1}+\stackrel{.}{l_2}+\stackrel{.}{l_3}=0$
$\Rightarrow -a_1-a_1+a_2=0$
$\Rightarrow a_2=2a_1$


Now, from the FBD's we have
$T-g=a_1$
$2T^{{}^{\prime }}=T$
And, $2g-T{}^{\prime }=2a_2=2\left(2a_1\right)$
From above equations, we have
$\frac{\begin{array}{c}T-g=a_1\\ 4g-T=8a_1\end{array}}{\begin{array}{c}3g=9a_1\\ \Rightarrow a_1=\frac{g}{3}\text{Upward}\\ \Rightarrow a_2=2a_1=\frac{2g}{3}\text{Downward}\end{array}}$