A modern gran -prix racing car of masses m is travelling on a flat track in a circular arc of radius R with a speed `v`. If the coefficient of static friction between the tyres and the track is `mu_(s)`, then the magnitude of negative lift `F_(L)` acting downwards on the car is `:` ( Assume forces on the four tyres are identical and g = acceleration due to gravity )

Options

A. `m (( v^(2))/( mu _(s) R) - g)`
B. ` - m ( g + ( v^(2))/( mu_(s) R))`
C. ` m (( v^(2))/( mu_(s) R) + g)`
D. ` m ( g - ( v^(2))/( mu_(s) R))`

Answer

A

Explanation

` ( mv^(2))/( r) = mu _(s) N`
`rArr N = ( mv ^(2))/( mu_(s) R)`
mg + F = N
F = N - mg
`F = ( m v^(2))/( mu_(s) R) - mg = m (( v^(2))/( mu _(s) R) - g)`