A car has to move on a level turn of radius $45 m$ . If the coefficient of static friction between the tyre and the road is $μ_{s} = 2.0$ , find the maximum speed the car can take without skidding.

40 m / s

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30 m / s

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20 m / s

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None of these

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Solution

The correct option is B $30 m / s$
$\begin{matrix} T h e c a r i s g o i n g o n a h o r i x o n t a l c i r c l e o f r a d i u s R, S o, i t i s a c c e l e r a t i n g ∴ a = \frac{v^{2}}{R} F o r v e r t i c a l d i r e c t i o n a = 0 t h e n, a c c o r d i n g t o q u e s t i o n t o n e w t o n^{'} s l a w F = m g = m a f_{i} = \frac{m v^{2}}{R} - - - (i) I n c a s e o f n o s k i d d i n g . f_{s} = μ_{s} F = μ_{s} m g - - - (i i) ∴ f r o m (i) & (i i) w e g e t μ_{s} m g = \frac{m v^{2}}{R} o r, v^{2} = μ_{s} g R v = \sqrt{2.0 \times 10 \times 45} = 30 m / s H e n c e, o p t i o n B i s t h e c o r r e c t a n s w e r . \end{matrix}$

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A car has to move on a level turn of radius 45m. If the coefficient of static friction between the tyre and the road is μs=2.0, find the maximum speed the car can take without skidding.

A car has to move on a level turn of radius $45 m$ . If the coefficient of static friction between the tyre and the road is $μ_{s} = 2.0$ , find the maximum speed the car can take without skidding.