Published by:
CGP EDU Academic Team
Published on: September 13, 2026
A motorcyclist wants to drive on the vertical surface of wooden ‘ well ’ of radius 5 m, in horizontal plane with speed of
m/s. Find the minimum value of coefficient of friction between the tyres and the wall of the well. (take g = 10 m/s 2 )
Text Solution
Verified by ExpertsThe correct answer is:
B
Step 1: Identify the parameters.
Radius of the well, r = 5 m
Speed of the motorcyclist, v = ? m/s (assumed to be V as given in the image, please confirm).
Gravitational acceleration, g = 10 m/s2.
Step 2: Use the centripetal force concept.
The centripetal force is provided by the frictional force and the weight of the motorcyclist acting on the wall.
Step 3: The frictional force, F_friction = BC * N, where N is the normal force.
Given that the motorcyclist's weight contributes to the normal force: N = m * g.
Step 4: For a body moving in a circular path, the centripetal force required is given as: F_centripetal = \frac{mv^2}{r}.
Therefore, equating the two forces: \u03BC * mg = \frac{mv^2}{r}.
Canceling m from both sides, we get: \u03BC * g = \frac{v^2}{r}.
Step 5: Solving for \u03BC: \u03BC = \frac{v^2}{rg}.
Substituting the known values: \u03BC = \frac{V^2}{5 * 10} = \frac{V^2}{50}.
Step 6: As we have assumed the minimum value of coefficient of friction between the tyres and the wall of the well requires specific value of speed. Please insert this known value of V in the equation to find \u03BC if provided. Therefore, using the proper V will yield the minimum coefficient of friction.
Radius of the well, r = 5 m
Speed of the motorcyclist, v = ? m/s (assumed to be V as given in the image, please confirm).
Gravitational acceleration, g = 10 m/s2.
Step 2: Use the centripetal force concept.
The centripetal force is provided by the frictional force and the weight of the motorcyclist acting on the wall.
Step 3: The frictional force, F_friction = BC * N, where N is the normal force.
Given that the motorcyclist's weight contributes to the normal force: N = m * g.
Step 4: For a body moving in a circular path, the centripetal force required is given as: F_centripetal = \frac{mv^2}{r}.
Therefore, equating the two forces: \u03BC * mg = \frac{mv^2}{r}.
Canceling m from both sides, we get: \u03BC * g = \frac{v^2}{r}.
Step 5: Solving for \u03BC: \u03BC = \frac{v^2}{rg}.
Substituting the known values: \u03BC = \frac{V^2}{5 * 10} = \frac{V^2}{50}.
Step 6: As we have assumed the minimum value of coefficient of friction between the tyres and the wall of the well requires specific value of speed. Please insert this known value of V in the equation to find \u03BC if provided. Therefore, using the proper V will yield the minimum coefficient of friction.
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