Question

Find the "Centrifuge effect" of the centrifuge, which spins at the angular velocity (\(\omega\)=523.6 /sec) at a maximum radius of 10 cm.

• A. 2794.6
• B. 2694.6
• C. 2594.6
• D. 2494.6

Hint:

The formula for centrifugal acceleration is $a_c = \omega^2 r$. To find the G-force, divide this by g (\(\approx\) 9.81 m/s$^2$). Always ensure your units are consistent (meters and radians/sec).

Answer 1

The Correct Option is A

Step 1: Define the "Centrifuge effect". This term typically refers to the G-force, which is the ratio of the centrifugal acceleration ($a_c$) to the acceleration due to gravity (g).

Step 2: Write the formula for centrifugal acceleration. \[ a_c = \omega^2 r \] where \(\omega\) is the angular velocity in radians per second and r is the radius in meters.

Step 3: Convert units and plug in the values. \(\omega\) = 523.6 rad/s (The unit /sec implies rad/sec as it's an angular velocity)
r = 10 cm = 0.1 m \[ a_c = (523.6 \text{ rad/s})^2 \times 0.1 \text{ m} = 274156.96 \text{ s}^{-2} \times 0.1 \text{ m} = 27415.7 \text{ m/s}^2 \]
Step 4: Calculate the G-force. Use g \(\approx\) 9.81 m/s$^2$. \[ \text{G-force} = \frac{a_c}{g} = \frac{27415.7 \text{ m/s}^2}{9.81 \text{ m/s}^2} \approx 2794.67 \] This value matches option (A).