What is 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 types and the road is 0.4 .(Given, acceleration due to gravity =`10 ms ^(-2)`

Options

A. `12ms^(-1)`
B. `10ms^(-1)`
C. `11ms^(-1)`
D. `15ms^(-1)`

Answer

C

Explanation

We know that for turning , centripetal force is provided by friction , so for the maximum speed, the centripetal force will be maximum .
` " " (mv^(2))/(r)ltF_L`
As `" " f_L=muN=mumg" "`(Where, N =mg)
Thus `," "(mv^(2))/(r)lemumg`
i.e `" "vlesqrtmugr,so thatv_(max)=sqrtmugr`
`" " `Here ,`mu=0.4,r=30m and g=10ms^(-2)`
so,`" " v_(max) =sqrt(0.4xx30xx10) rArr V_(max)~~11ms^(-1)`