Question

A car starts rest, on a horizontal circular road of radius R, the tangential acceleration of the car is a. The friction coefficient between the road and the tyre is `mu` Find the speed at which car will skid and also find the distance after travelling it skids.

Answer 1

Correct Answer - A::B::D
Since the motion is non uniform, the acceleration has both radial and tangential components.
`a=v^2/r`
`a_t=(dv)/(dt)=a`
Resultnt magnitude = `sqrt((v^2/r)^2+a^2)`
`Now, mN=msqrt((v^2/r)^2+a^2`
`rarr mumg=msqrt((v^2/r)^2+a^2`
`rarr mu^2g^2=v^4/r^2+a^2`

`rarr v^4/r^2=(mu^2g^2-a^2)`
`rarr v^4=(mu^2g^2-a^2)r^2`
`rarr v=[(m^2g^2-a^2)r^2]^)1/4)`