In a simple Atwood machine, two unequal masses m_1 and m_2 are...

Given:
$m_1 = 300 \text{ g} = 0.3 \text{ kg}$
$m_2 = 600 \text{ g} = 0.6 \text{ kg}$
Acceleration due to gravity, $g = 9.8 \text{ m/s}^2$

The tension $T$ in the string of a simple Atwood machine is given by:
$T = \dfrac{2 m_1 m_2}{m_1 + m_2} g$

Substituting the given values:
$T = \dfrac{2 \times 0.3 \times 0.6}{0.3 + 0.6} \times 9.8$
$T = \dfrac{0.36}{0.9} \times 9.8$
$T = 0.4 \times 9.8 = 3.92 \text{ N}$

The pulley is light (massless), so the net force on it is zero. The upward force exerted by the clamp on the pulley must balance the total downward force acting on the pulley due to the tension in the two segments of the string.

Force exerted by the clamp $= 2T$
$F = 2 \times 3.92 \text{ N}$
$F = 7.84 \text{ N} \approx 7.8 \text{ N}$