A coin placed on a rotating table just slips when it is placed at a distance of 1 cm from the center. If the angular velocity of the table is halved, it will just slip when placed at a distance of ______ from the centre. [2023]

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Solution

Q.
A coin placed on a rotating table just slips when it is placed at a distance of 1 cm from the center. If the angular velocity of the table is halved, it will just slip when placed at a distance of ______ from the centre. [2023]

1 2 cm

2 1 cm

3 8 cm

4 4 cm

Ans.
(4)

$f_{s max} = μ m g = m ω^{2} R \Rightarrow R = \frac{μ g}{ω^{2}}$

So if $ω$ becomes $\frac{ω}{2}$ , $R$ will become $4 R$ .

So distance from the center will be 4 cm.

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