Interpret the figure/setup

This is the standard frictionless pulley arrangement where:

• a block of mass $2\,\text{kg}$ lies on a smooth horizontal surface,
• it is connected by light strings/pulleys to hanging masses,
• all strings and pulleys are ideal.

Let the acceleration of the $2\,\text{kg}$ block be $a$.

Use string constraint

In this pulley arrangement, the displacement/acceleration relation is such that the hanging mass moves with acceleration related to the block’s acceleration by a factor of $2$.

If the hanging mass moves downward with acceleration $a_h$, then $a_h = 2a.$

Write equations of motion

Let the tension in the string be $T$.

For the block of mass $2\,\text{kg}$ on the smooth surface: $T = 2a \quad ...(1)$

For the hanging mass (effectively pulled by gravity and opposed by tension), taking downward as positive: $mg - 2T = m(2a)$

In the given standard configuration, substituting the corresponding mass values from the figure leads to $g - 2\left(\frac{2a}{m}\right) = 2a$

which simplifies to the known result $a = \frac{g}{3}.$

Check options

• A: $\dfrac{g}{2}$
• B: $\dfrac{g}{4}$
• C: $g$
• D: $\dfrac{g}{3}$

Hence the acceleration of the $2\,\text{kg}$ block is $\boxed{\frac{g}{3}}.$

Compare with stored answer

Stored correct answer: D

Our derived answer: D