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A toy car of mass $m$ can travel at a fixed speed. It moves in a circle on a fixed horizontal table. A string is connected to the car and attached to a block of mass $M$ that hangs as shown in figure (the portion of string below the table is always vertical). The coefficient of friction between the surface of table and tyres of the toy car is $μ$ . Find the ratio of the maximum radius to the minimum radius for which the toy car can move in a circular path with centre $O$ on table. (Given $M = 3 k g; m = 2 k g; μ = 1 / 2$ )

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Detailed Solution

If $m g > \frac{m v^{2}}{r}$ ,friction force acts outwards

$T - μ m g = \frac{m v^{2}}{r_{m a x}}$

If $m g < \frac{m v^{2}}{r}$ fractional force on car towards centre

$T - μ m g = \frac{m v^{2}}{r_{m i n}}$

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