A coin, placed on a rotating turn-table slips, when it is placed at a distance of $9 \,cm$ from the centre. If the angular velocity of the turn-table is trippled, it will just slip, if its distance from the centre is ......... $cm$.
A coin, placed on a rotating turn-table slips, when it is placed at a distance of $9 \,cm$ from the centre. If the angular velocity of the turn-table is trippled, it will just slip, if its distance from the centre is ......... $cm$.
$27$
$9 $
$3 $
$1$
A coin, placed on a rotating turn-table slips, when it is placed at a distance of $9 \,cm$ from the centre. If the angular velocity of the turn-table is trippled, it will just slip, if its distance from the centre is ......... $cm$.
In the given condition friction provides the required centripetal force and that is constant. i.e. $mw^{2}r=$constant
$⇒$ $r \propto \frac{1}{{{\omega ^2}}}$ $⇒$ ${r_2} = {r_1}{\left( {\frac{{{\omega _1}}}{{{\omega _2}}}} \right)^2} = 9{\left( {\frac{1}{3}} \right)^2} = 1\,cm$