Question

A bus turns on an unbanked rough road having
coefficient of friction 0.4 with a speed of 5 m/s. The
minimum radius of the arc in which bus turns safely
without skidding is
[Take g = 10 m/s]
​

Answer 1

Answer:

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Answer 2

Given:

A bus turns on an unbanked rough road having coefficient of friction 0.4 with a speed of 5 m/s.

To find:

The minimum radius of the arc in which the bus can turn safely without being skid off the road.

Calculation:

The basic concept in this type of questions is that:

• In limiting conditions, the centrifugal force experienced by the bus during turning on that arc will be equal and opposite to the static friction.

$\rm{ \therefore \: centifugal \: force = friction}$

$\rm{ = > \dfrac{m {v}^{2} }{r} = \mu(normal \: reaction)}$

$\rm{ = > \dfrac{m {v}^{2} }{r} = \mu(mg)}$

$\rm{ = > \dfrac{ {v}^{2} }{r} = \mu g}$

$\rm{ = > r = \dfrac{ {v}^{2} }{ \mu g} }$

$\rm{ = > r = \dfrac{ {(5)}^{2} }{0.4 \times 10} }$

$\rm{ = > r = \dfrac{ 25}{4 } }$

$\rm{ = > r = 6.25 \: m }$

So, final answer is:

$\boxed{ \bf{ radius \: of \: arc = 6.25 \: m }}$