Question

A disc of mass 10 kg and radius 0.1 m/s rotating at 120 r.p.m. A retarding torque brings it to rest in 10s. If the same torque is due to force applied tangentially on the rim of the disc then magnitude of force is ______.

Options

• 0.1 πN

• 0.2 πN

• 0.4 πN

• 0.8 πN

Answer 1

A disc of mass 10 kg and radius 0.1 m/s rotating at 120 r.p.m. A retarding torque brings it to rest in 10s. If the same torque is due to force applied tangentially on the rim of the disc then magnitude of force is 0.2 πN.

Explanation:

frequency f = 120 rpm `=120/60=2 "rps"`

ω = 2πf = 2π × 2 = 4π rad/s

Angular acceleration `=prop=(omega_2-omega_1)/t=(0-4pi)/10=(-2pi)/5  "rad/s"^2`

Moment of inertia `"I"="MR"^2/2=(10xx(0.1)^2)/2=0.05  "kg m"^2`

Torque `tau="I"alpha=0.05xx2/5pi=0.02pi  "Nm"`

τ = Fr

`therefore"F"=tau/r=(0.02pi)/0.1=0.2pi  "N"`