The velocity at which 6 kg mass (shown in figure) strikes the...

Let the acceleration of the system be $a$ and the tension in the string be $T$.

The equations of motion for the two masses are:
$6g - T = 6a$
$T - 2g = 2a$

Adding the two equations, we get:
$4g = 8a$
$\Rightarrow a = \dfrac{4g}{8} = \dfrac{g}{2}$

Substituting $g = 10 \text{ m/s}^2$, the acceleration is:
$a = \dfrac{10}{2} = 5 \text{ m/s}^2$

The $6 \text{ kg}$ mass is released from rest ($u = 0$) and travels a downward distance $s = 6 \text{ m}$.

Using the kinematic equation $v^2 = u^2 + 2as$:
$v^2 = 0 + 2 \times 5 \times 6$
$v^2 = 60$
$v = \sqrt{60} \approx 7.74 \text{ m/s}$

Answer: $7.74$