A coin placed on a rotating table just slips when it is placed at a...

The coin will slip when

$\mumg = m{\omega}^{2}r$

$⇒ \mug = {\omega}^{2} \times 1cm . . . ( i )$

Now, $\omega ' = \dfrac{\omega}{2}$

$\mug = {\left(\dfrac{\omega}{2}\right)}^{2}R . . . ( ii )$

Hence we can write from (i) and (ii)

${\omega}^{2} \times 1cm = \dfrac{{\omega}^{2}}{4}R ⇒ R = 4cm$