A uniform disc of mass 300kg is rotating freely about a vertical axis through its centre at a constant angular velocity ω o . A boy of mass 30kg starts from the centre and moves along a radius to the edge of the disc. Angular velocity of the disc will now become

Question

A uniform disc of mass 300kg is rotating freely about a vertical axis through its centre at a constant angular velocity ω o . A boy of mass 30kg starts from the centre and moves along a radius to the edge of the disc. Angular velocity of the disc will now become (A) (ω o/6) (B) (ω o/5) (C) (4 ω o/5) (D) (5 ω o/6)

Tardigrade Admin · Accepted Answer

As Sigma τ=0, angular momentum remains conseved: ∴ L=(0 + (300 R2/2))(ω )0=((300 R2/2) + 30 R2)ω ⇒ 150ω 0=180ω ⇒ ω =(5/6)ω 0

Q. A uniform disc of mass $300 k g$ is rotating freely about a vertical axis through its centre at a constant angular velocity $ω_{o}$ . A boy of mass $30 k g$ starts from the centre and moves along a radius to the edge of the disc. Angular velocity of the disc will now become

$\frac{ω _{o}}{6}$

$\frac{ω _{o}}{5}$

$\frac{4 ω _{o}}{5}$

$\frac{5 ω _{o}}{6}$

As $Σ τ = 0,$ angular momentum remains conseved:
$∴ L = (0 + \frac{300 R ^{2}}{2}) (ω)_{0} = (\frac{300 R ^{2}}{2} + 30 R^{2}) ω$
$\Rightarrow 150 ω_{0} = 180 ω \Rightarrow ω = \frac{5}{6} ω_{0}$

Q. A uniform disc of mass 300kg is rotating freely about a vertical axis through its centre at a constant angular velocity ωo​ . A boy of mass 30kg starts from the centre and moves along a radius to the edge of the disc. Angular velocity of the disc will now become

6ωo​​

5ωo​​

54ωo​​

65ωo​​