JEEAdvanced
A car travels on a curved road of radius 50 m that is banked at an…
Question
A car travels on a curved road of radius 50 m that is banked at an angle whose tangent is 0.75. The coefficient of friction between the tyres and the road is 0.5 and g = 10 m/s^2. Find the square of the maximum speed (in m^2/s^2) at which the car can negotiate the curve without skidding outward.
✓ Verified answer: 1000checked by our engine — not a guess
Step-by-step solution
At maximum speed, friction acts down the bank (preventing the car sliding up/out).
Resolving along and perpendicular to the incline and eliminating the normal force gives v_max^2 = g R (tan theta + mu)/(1 - mu tan theta).
With R = 50, g = 10, tan theta = 0.75, mu = 0.5: v_max^2 = 10*50*(0.75 + 0.5)/(1 - 0.5*0.75) = 500*(1.25)/(0.625) = 625/0.625 = 1000 m^2/s^2.
Final answer1000
Stuck on a problem like this?
Paste any JEE or NEET question — verified working, a confidence %, and an honest “not sure” instead of a bluff.
Solve my doubt →More Physics Mechanics solutions
A wedge of mass M = 4 kg with a smooth inclined face making 45…JEE · PhysicsA block of mass 2 kg moving at 10 m/s slides onto the left end of a…JEE · PhysicsA particle is projected from the foot of a fixed inclined plane whose…JEE · PhysicsA thin uniform rod of mass M and length L is hinged at one end about…JEE · PhysicsA small particle is placed at rest on the very top of a fixed smooth…JEE · PhysicsOn a frictionless horizontal line, a ball A of mass m moves with…JEE · PhysicsA solid uniform sphere (moment of inertia 2/5 M R^2 about its centre)…JEE · PhysicsA uniform flexible chain of total length 2 m lies on a frictionless…JEE · Physics