A disc of mass 2 kg and radius 0.2 m is rotating with angular velocity 30 rad/s. What is angular velocity, if a mass of 0.25 kg is put on periphery of the disc?

Question

A disc of mass 2 kg and radius 0.2 m is rotating with angular velocity 30 rad/s. What is angular velocity, if a mass of 0.25 kg is put on periphery of the disc? (A) 24 rad/s (B) 36 rad/s (C) 15 rad/s (D) 26 rad/s

Tardigrade Admin · Accepted Answer

If no external torque acts on a system of particles, then angular momentum of the system remains constant, that is

τ = 0

\Rightarrow \frac{d L}{d t} = 0

\Rightarrow L = I ω =

constant

\Rightarrow I_{1} ω_{1} = I_{2} ω_{2}

hence

\frac{1}{2} M r^{2} ω_{1} = \frac{1}{2} (M + 2 m) r^{2} ω_{2}

.....(i)
Here

M = 2 K g, m = 0.25 k g, r = 0.2 m

,

ω_{1} = 30 r a d s^{- 1}

Hence, we get after putting the given values in Eq. (i)

\frac{1}{2} \times 2 \times (0.2)^{2} \times 30

= \frac{1}{2} \times (2 + 2 \times 0.25) (0.2)^{2} \times ω_{2}

or

1.2 = 0.05 ω_{2}

or

1.2 = 0.05 ω_{2}

or

ω_{2} = 24 r a d s^{- 1}

Q. A disc of mass 2kg and radius 0.2m is rotating with angular velocity 30rad/s. What is angular velocity, if a mass of 0.25kg is put on periphery of the disc?

24 rad/s

36 rad/s

15 rad/s

26 rad/s

Q. A disc of mass $2 k g$ and radius $0.2 m$ is rotating with angular velocity $30 r a d / s$ . What is angular velocity, if a mass of $0.25 k g$ is put on periphery of the disc?