Question

A coin placed on a rotating turn table just slips if it is at a distance of $40cm$ from the centre if the angular velocity of the turntable is doubled, it will just slip at a distance of:

• A. $10cm$
• B. $20cm$
• C. $40cm$
• D. $80cm$

Answer 1

The correct option is A $10cm$

It slips when.
$\mu mg=m{\omega }^{2}r$
$\Rightarrow \mu g={\omega }^{2}r$
$\Rightarrow \mu g={\omega }^{2}40......\left(1\right)$
$Now,\omega =2\omega$
$\Rightarrow \mu g={\left(2\omega \right)}^{2}r\Rightarrow 4{\omega }^{2}r.....\left(2\right)$
$\therefore {\omega }^2\times 40=4{\omega }^{2}r$
$\Rightarrow r=10cm$