A ceiling fan operates at 1500 rpm at full speed and has a diameter...

The angular velocity of the fan is given by:

$\omega = \dfrac{2\pi N}{60} = \dfrac{2\pi \times 1500}{60} = 50\pi \text{ rad/s}$

The radius of the circular path is $r = \dfrac{120}{2} = 60 \text{ cm} = 0.6 \text{ m}$.

The mass of the particle is $m = 1 \text{ g} = 10^{-3} \text{ kg}$.

The force experienced by the particle is the centripetal force required to keep it in circular motion, which is provided by the blade:

$F = m\omega^2 r = 10^{-3} \times (50\pi)^2 \times 0.6$

$F = 10^{-3} \times 2500\pi^2 \times 0.6 = 1.5\pi^2 \text{ N}$

Using $\pi^2 \approx 9.87$, we get:

$F \approx 1.5 \times 9.87 = 14.8 \text{ N}$

By Newton's third law of motion, the particle exerts an equal and opposite force on the blade. Since the centripetal force acts radially inwards along the surface of the blade, the reaction force exerted by the particle acts radially outwards along the surface of the blade.

Thus, the magnitude of the force exerted by the particle on the blade is also $14.8 \text{ N}$.