The velocity at which 6 kg mass (shown in figure) strikes the ground when it is released from a height of 6 m above the ground is __________ m/s. Assume pulley is massless and string is light and inextensible. (Take $$g = 10$$ m/s$$^2$$)

The downward acceleration of the $$6\text{ kg}$$ mass is given by:

$$a = \left( \frac{m_1 - m_2}{m_1 + m_2} \right) g$$

$$a = \left( \frac{6 - 2}{6 + 2} \right) \times 10 = \left( \frac{4}{8} \right) \times 10 = 5\text{ m/s}^2$$

The block starts from rest ($$u = 0$$) and falls through a height distance ($$s$$) = $$6\text{ m}$$

$$v^2 = u^2 + 2as$$

$$v^2 = 0 + 2(5)(6) = 60$$

$$v = \sqrt{60} \approx 7.7459\text{ m/s}$$