To find the centripetal force acting on a particle fixed to the tip of a rotating fan blade, we can use the formula for centripetal force, which is given by: \[ F_c = m \cdot a_c \] where: - \( F_c \) is the centripetal force, - \( m \) is the mass of the particle, - \( a_c \) is the centripetal acceleration. The centripetal acceleration can be calculated using the formula: \[ a_c = r \cdot \omega^2 \] where: - \( r \) is the radius of the circular path, - \( \omega \) is the angular velocity in radians per second. ### Step-by-Step Calculation 1. **Identify the given values:** - Mass \( m = 10^{-2} \) kg (which is 0.01 kg), - Angular velocity \( \omega = 100 \) rad/s, - Radius \( r = 0.2 \) m. 2. **Calculate the centripetal acceleration \( a_c \):** \[ a_c = r \cdot \omega^2 \] Substituting the values: \[ a_c = 0.2 \, \text{m} \cdot (100 \, \text{rad/s})^2 \] \[ a_c = 0.2 \, \text{m} \cdot 10000 \, \text{(rad/s)}^2 \] \[ a_c = 2000 \, \text{m/s}^2 \] 3. **Calculate the centripetal force \( F_c \):** \[ F_c = m \cdot a_c \] Substituting the values: \[ F_c = 0.01 \, \text{kg} \cdot 2000 \, \text{m/s}^2 \] \[ F_c = 20 \, \text{N} \] ### Conclusion The centripetal force acting on the particle is **20 N**. Therefore, the correct option is **B**. ### Explanation of Other Options - **Option A (2 N):** This value is too low. It does not account for the high angular velocity and the radius of the circular path. - **Option C (200 N):** This value is too high. It seems to miscalculate the centripetal acceleration or the mass. - **Option D (400 N):** This value is also too high and likely results from a misunderstanding of the relationship between mass, radius, and angular velocity. ### Revision Summary - Centripetal force is calculated using \( F_c = m \cdot a_c \). - Centripetal acceleration is given by \( a_c = r \cdot \omega^2 \). - Always ensure units are consistent (mass in kg, radius in m, angular velocity in rad/s). - For this problem, the correct centripetal force is **20 N**.