A disc of mass 2 kg and radius 0.2m is rotating with an angular velocity 30 rads- 1 , about an axis passing through its centre and perpendicular to its plane. If a mass of 0.25 kg is stuck on the periphery of the disc, then its angular velocity will become

Question

A disc of mass 2 kg and radius 0.2m is rotating with an angular velocity 30 rads- 1 , about an axis passing through its centre and perpendicular to its plane. If a mass of 0.25 kg is stuck on the periphery of the disc, then its angular velocity will become (A) 24 rad s- 1 (B) 36 rad s- 1 (C) 15 rad s- 1 (D) 26 rad s- 1

Tardigrade Admin · Accepted Answer

When there is no external torque then the angular momentum remains constant.
i.e.

τ = 0 \Rightarrow \frac{d L}{d t} = 0

∴ I_{1} ω_{1} = I_{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, putting the value of

ω_{1}

in equation (i), we get

\Rightarrow \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}

\Rightarrow 1.2 = 0.05 ω_{2}

\Rightarrow ω_{2} = 24 r a d s^{- 1}

Q. A disc of mass $2 k g$ and radius $0.2 m$ is rotating with an angular velocity $30 r a d s^{- 1}$ , about an axis passing through its centre and perpendicular to its plane. If a mass of $0.25 k g$ is stuck on the periphery of the disc, then its angular velocity will become

$24 r a d s^{- 1}$

$36 r a d s^{- 1}$

$15 r a d s^{- 1}$

$26 r a d s^{- 1}$

Q. A disc of mass 2kg and radius 0.2m is rotating with an angular velocity 30rads−1 , about an axis passing through its centre and perpendicular to its plane. If a mass of 0.25kg is stuck on the periphery of the disc, then its angular velocity will become

24rads−1

36rads−1

15rads−1

26rads−1

Q. A disc of mass $2 k g$ and radius $0.2 m$ is rotating with an angular velocity $30 r a d s^{- 1}$ , about an axis passing through its centre and perpendicular to its plane. If a mass of $0.25 k g$ is stuck on the periphery of the disc, then its angular velocity will become

$24 r a d s^{- 1}$

$36 r a d s^{- 1}$

$15 r a d s^{- 1}$

$26 r a d s^{- 1}$