Keeping the angle of banking, unchanged if the radius of curvature is made four times , the percentages increase in the maximum speed with which a vehicle can travel on a circular road is Correct answer_100·/. How to solve?

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Answer

Solving for the Percent Increase in Maximum Speed on a Circular Road

To solve for the percentage increase in maximum speed on a circular road while keeping the angle of banking unchanged, follow these steps:

Understand the concept of angle of banking and its relation to speed on a circular road. The angle of banking is the angle at which a road is inclined towards the center of the circular path. It is designed to counteract the centrifugal force acting on a vehicle as it travels on the curve. The greater the speed of the vehicle, the greater the centrifugal force and the steeper the angle of banking required to keep the vehicle on the road.

Know the formula for determining the maximum speed on a circular road. The maximum speed of a vehicle on a circular road is directly proportional to the square root of the radius of curvature of the road and inversely proportional to the angle of banking. V = sqrt(Rg/tanθ), where V is the maximum speed, R is the radius of curvature, g is the acceleration due to gravity, and θ is the angle of banking.

Substitute the given values into the formula. Let the original radius of curvature be R and the new radius of curvature be 4R. Since the angle of banking is unchanged, it remains θ. Therefore, the original maximum speed is V1 = sqrt(Rg/tanθ) and the new maximum speed is V2 = sqrt((4R)g/tanθ).

Simplify the formula for the new maximum speed. V2 = sqrt((4R)g/tanθ) = sqrt(4Rg/tanθ) = 2sqrt(Rg/tanθ). Therefore, the new maximum speed is twice the original maximum speed.

Calculate the percentage increase in maximum speed. The percentage increase is (V2 - V1)/V1 x 100%. Substituting the values, (2V1 - V1)/V1 x 100% = 100%. Therefore, the percentage increase in maximum speed is 100%.

Therefore, if the radius of curvature is made four times while keeping the angle of banking unchanged, the maximum speed with which a vehicle can travel on a circular road increases by 100%.

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