Question

Consider the situation shown in figure. Both the pulleys and the string are light and all the surfaces are smooth. Find the acceleration of $1kg$ block.

• A. $\frac{2g}{3}$
• B. $g$
• C. $2g$
• D. $3g$

Answer 1

The correct option is A $\frac{2g}{3}$

Let the displacement of blocks of mass 1kg and 2kg be $x_1$ and $x_2$ respectively.

Using work theorem : $2T{x}_2-T{x}_1=0$

$\therefore$ $x_1=2x_2$

Differentiating twice w.r.t time we get, $2a_2=a_1$ $⟹a_2=\frac{a}{2}$

For block of mass 2 kg : $2\left(a/2\right)=2T$ $⟹a=2T$

For block of mass 1 kg : $a=g-T$

$\therefore$ $a=g-\frac{a}{2}$ $⟹a=\frac{2g}{3}$