Question

A horizontal circular platform of mass M is rotating at angular velocity ω about a vertical axis passing through its centre. A boy of mass m is standing at the edge of the platform. If the boy comes to the centre of the platform, then the new angular velocity becomes ______.

पर्याय

• `(1 + m/M)omega`

• `(1 - m/M)omega`

• `(1 + m/(2M))omega`

• `(1 + (2m)/M)omega`

Answer 1

A horizontal circular platform of mass M is rotating at angular velocity ω about a vertical axis passing through its centre. A boy of mass m is standing at the edge of the platform. If the boy comes to the centre of the platform, then the new angular velocity becomes `underlinebb((1 + (2m)/M)omega)`.

Explanation:

Initially, the moment of inertia of the system at A,

`l_i = mR^2 + (MR^2)/2 = ((2m + M)/2)R^2`

Finally, the moment of inertia of the system will become,

`l_f = (MR^2)/2`

By conservation of angular moment about 0,

`L_i = L_f`

⇒ `l_iomega_i = l_fomega_f`

⇒ `omega_f = l_i/l_f omega = ((2m + M)/2)R^2 xx 2/(MR^2) xx omega = (1 + (2m)/M)omega`