Question

If the radius is doubled and angular speed is reduced to half of its original value, the centrifugal force relative to its original value is
1. 2 times
2. 0.5 times
3. 0.2 times
4. 0.1 times

Answer 1

Correct Answer - Option 2 : 0.5 times

Concept:

Centrifugal force: The imaginary force acting on the particle moving on a circular path after observing with respect to the particle itself is called centrifugal force.

\(Centrifugal\;force\;\left( F \right) =~\frac{mV_c^2}{r}\)

Also, V_c = rω

∴ F = mrω² 

where m is mass of the particle, V_c = velocity, r = radius, ω = angular velocity 

Explanation:

Given:

r₂ = 2r₁, \(ω_2~=~\frac{ω_1 }{2}\)

Therefore, by using the above value we have,

\(\frac{F_2}{F_1}~=~\frac{mr_2\omega_2^2}{mr_1\omega_1^2}~=~\frac{2r_1(\frac{\omega_1}{2})^2}{r_1\omega_1^2}\)

F₂ = 0.5 × F₁