Question

A block of mass $m$ is kept on a horizontal turntable at $x$ distance from the centre. If the coefficient of friction between the block and surface of turntable is $\mu$, then maximum angular speed of the table so that block does not slip

• A. $\sqrt{\frac{\mu g}{x^2}}$
• B. $\sqrt{\frac{\mu g}{x}}$
• C. $\sqrt{\frac{\mu g}{2x}}$
• D. $\sqrt{\frac{\mu x^2}{g}}$

Answer 1

The correct option is B $\sqrt{\frac{\mu g}{x}}$

Hence, option $B$ is correct answer.

If the block does not slip

Friction = Centripetal force

$\mu N=m{\omega }^{2}r$

$\therefore \mu g={\omega }^{2}x$

$\therefore \omega =\sqrt{\frac{\mu g}{x}}$