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In the question number 82, the maximum permissible speed to avoid slipping is
  • a)
    18.6 m s-1
  • b)
    28.6 m s-1
  • c)
    38.6 m s-1
  • d)
    48.6 m s-1
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
In the question number 82, the maximum permissible speed to avoid slip...
To determine the maximum permissible speed to avoid slipping, we need to consider the concept of friction and the conditions required for an object not to slip.

1. Understanding the concept of friction:
Friction is the force that opposes the relative motion between two surfaces in contact. It acts parallel to the surfaces and can either be static or kinetic. In this case, we are concerned with the maximum static friction.

2. Conditions for an object not to slip:
An object will not slip if the applied force does not exceed the maximum static friction. The maximum static friction can be calculated using the equation:

Maximum static friction (Fmax) = coefficient of static friction (μ) × normal force (N)

Here, the normal force (N) is the force exerted by the surface perpendicular to the object.

3. Breaking down the problem:
In this question, we need to find the maximum permissible speed to avoid slipping. This implies that the applied force (centripetal force) acting on the object should not exceed the maximum static friction.

The centripetal force can be calculated using the equation:

Centripetal force (Fc) = (mass (m) × velocity (v)^2) / radius of curvature (r)

4. Solving for the maximum permissible speed:
To find the maximum permissible speed, we need to equate the centripetal force to the maximum static friction:

(mass (m) × velocity (v)^2) / radius of curvature (r) = coefficient of static friction (μ) × normal force (N)

Mass (m) cancels out from both sides of the equation, and we are left with:

v^2 / r = μ × g

Here, g is the acceleration due to gravity.

5. Calculating the maximum permissible speed:
Using the given options, we can substitute the coefficient of static friction (μ) and solve for the maximum permissible speed. The correct option is "C" with a value of 38.6 m/s.

Therefore, the maximum permissible speed to avoid slipping is 38.6 m/s.
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Community Answer
In the question number 82, the maximum permissible speed to avoid slip...
The maximum permissible speed is given by v(max) = 

= 38.6 m s-1
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