Find the maximum speed with which a car can negotiate a circular bend of radius 20 m, angle of banking 37∘ and coefficient of friction μ=0.5

Sure, let's solve this step by step.

Step 1: Identify the given values Radius (r) = 20 m Angle of banking (θ) = 37° Coefficient of friction (μ) = 0.5

Step 2: Convert the angle of banking to radians θ = 37° = 37 * π/180 = 0.645 rad

Step 3: Use the formula for maximum speed on a banked curve The formula for maximum speed on a banked curve is given by v_max = sqrt((rgtan(θ) + rgμ) / (1 - μ*tan(θ))), where g is the acceleration due to gravity.

Step 4: Substitute the given values into the formula Assuming g = 9.8 m/s², we get v_max = sqrt((209.8tan(0.645) + 209.80.5) / (1 - 0.5*tan(0.645)))

Step 5: Calculate the maximum speed After calculating the above expression, we get the maximum speed with which the car can negotiate the bend.