Why is it important to have a balanced centrifuge?

It is important to properly balance a centrifuge because an unbalanced machine can damage the rotor, cause catastrophic damage to the machine itself, or even injure or kill lab personnel working in the room. Balancing a centrifuge involves spreading the weight of the samples across the entire rotor.

initial speed when it is dropped is 150 ft/s

now at the same moment the acceleration due to gravity is perpendicular to its velocity

so as we know that

now we have centripetal acceleration a = 32 ft/s^2 as its perpendicular to velocity

while tangential acceleration at the same moment will be zero

so

now radius of curvature is given as

so the radius of curvature just after it is dropped is 703.125 ft