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A modern grand - prix racing car of mass 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)
Option: 1 -m\left ( g+\frac{v^{2}}{\mu _{s}R} \right )
Option: 2 m\left ( g-\frac{v^{2}}{\mu _{s}R} \right )
Option: 3 m\left (\frac{v^{2}}{\mu _{s}R}-g \right )  
Option: 4 m\left (\frac{v^{2}}{\mu _{s}R}+g \right )

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\begin{array}{l} \mu_{\mathrm{s}} \mathrm{N}=\frac{\mathrm{mv}^{2}}{\mathrm{R}} \\ \\ \mathrm{N}=\frac{\mathrm{mv}^{2}}{\mu_{\mathrm{s}} \mathrm{R}}=\mathrm{mg}+\mathrm{F}_{\mathrm{L}} \\ \\ \mathrm{F}_{\mathrm{L}}=\frac{\mathrm{mv}^{2}}{\mu_{\mathrm{s}} \mathrm{R}}-\mathrm{mg} \end{array}

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avinash.dongre

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