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The maximum speed at which a car can turn round a curve of 400 m radius on a level road is: (Given: coefficient of friction between the tyres and road is 0.1, and g = 10 m/s2)
- a)20 m/s
- b)14 m/s
- c)26 m/s
- d)21 m/s
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
The maximum speed at which a car can turn round a curve of 400 m radiu...
When the car moves in a curvature of radius R, the force acting towards the centre of curvature must be equal to mv2/R
where m is mass of the car, v is the speed of car
But when we draw the free body diagram of the car the only force towards the centre of curvature is the friction force which is f = μmg
Hence by comparing we get v = √μgR
Substituting values gives, v= 20ms-1
where m is mass of the car, v is the speed of car
But when we draw the free body diagram of the car the only force towards the centre of curvature is the friction force which is f = μmg
Hence by comparing we get v = √μgR
Substituting values gives, v= 20ms-1
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Given Data:
- Radius of the curve, r = 400 m
- Coefficient of friction, μ = 0.1
- Acceleration due to gravity, g = 10 m/s²
Formula used:
The maximum speed at which a car can turn around a curve without slipping is given by:
\[ v = \sqrt{μ \cdot g \cdot r} \]
Calculation:
Given r = 400 m, μ = 0.1, and g = 10 m/s²
Substitute the values in the formula:
\[ v = \sqrt{0.1 \times 10 \times 400} \]
\[ v = \sqrt{400} \]
\[ v = 20 m/s \]
Therefore, the maximum speed at which the car can turn around the curve of 400 m radius is 20 m/s. Hence, option A is the correct answer.
- Radius of the curve, r = 400 m
- Coefficient of friction, μ = 0.1
- Acceleration due to gravity, g = 10 m/s²
Formula used:
The maximum speed at which a car can turn around a curve without slipping is given by:
\[ v = \sqrt{μ \cdot g \cdot r} \]
Calculation:
Given r = 400 m, μ = 0.1, and g = 10 m/s²
Substitute the values in the formula:
\[ v = \sqrt{0.1 \times 10 \times 400} \]
\[ v = \sqrt{400} \]
\[ v = 20 m/s \]
Therefore, the maximum speed at which the car can turn around the curve of 400 m radius is 20 m/s. Hence, option A is the correct answer.
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