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Physics-

General

Easy

Question

Find the maximum speed at which a car can turn round a curve of 30 m radius on a level road if the coefficient of friction between the tyres and the road is 0.4
(Acceleration due to gravity $equals 10 blank m s to the power of negative 2 end exponent right parenthesis$

$12 {m s}^{- 2}$
$10 {m s}^{- 2}$
$11 {m s}^{- 2}$
$15 {m s}^{- 2}$

The correct answer is: $11 blank m s blank to the power of negative 2 end exponent$

Centripetal force is provided by friction, so
$fraction numerator m v to the power of 2 end exponent over denominator r end fraction less than f subscript L end subscript blank i e comma fraction numerator m v to the power of 2 end exponent over denominator r end fraction less than mu blank m g$
$i. e comma blank v less than square root of mu g r end root s o blank t h a t comma blank v subscript m a x end subscript equals square root of mu g r end root$
$H e r e comma blank mu equals 0.4 comma blank r equals 30 m blank a n d blank g equals 10 m s to the power of negative 2 end exponent$
$therefore blank v subscript m a x end subscript equals square root of 0.4 cross times 30 cross times 10 end root equals 11 m divided by s$

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