Question

A small object placed on a rotating horizontal turn table just slips when it is placed at a distance 4 cm from the axis of rotation. If the angular velocity of the turn-table is doubled, the object slips when its distance from the axis of rotation is :

• A. 1 cm
• B. 2 cm
• C. 4 cm
• D. 8 cm

Answer 1

Answer: (A)

1 cm

Answer 2

The object will slip if centripetal force $\geq$ force of friction

$m r \omega ^ { 2 } \geq \mu m g$

$r \omega ^ { 2 } \geq \mu g$

$m r \omega ^ { 2 } \geq c o n s \tan t$

Or $\left( \frac { r _ { 1 } } { r _ { 2 } } \right) = \left( \frac { \omega _ { 21 } } { \omega _ { 1 } } \right) ^ { 2 }$

$\frac { 4 \mathrm {~cm} } { r _ { 2 } } = \left( \frac { 2 \omega } { \omega } \right) ^ { 2 } \therefore r _ { 2 } = 1 \mathrm {~cm}$