Question

In case of well of death which is a vertical cylindrical wall of radius ' \(r\) ' inside which vehicle is driven in horizontal circles. If ' \(m\) ' is mass of vehicle, ' \(V\) ' is the velocity and ' \(\mu_s\) ' is the coefficient of static friction between the wheels of vehicle and walls then correct relation is [ \(g\) = acceleration due to gravity]

• A. \(V^2 \le \frac{rg}{\mu_s}\)
• B. \(V \le \frac{rg}{\mu_s}\)
• C. \(V^2 \ge \frac{rg}{\mu_s}\)
• D. \(V \ge \frac{rg}{\mu_s}\)

Hint:

Well of death: Friction supports weight

Answer 1

The Correct Option is C

Concept: For circular motion: \[ \text{Normal force} = \frac{mv^2}{r} \] Friction balances weight: \[ \mu_s N \ge mg \]

Step 1: Substitute $N$. \[ \mu_s \cdot \frac{mv^2}{r} \ge mg \]

Step 2: Simplify. \[ v^2 \ge \frac{rg}{\mu_s} \]

Step 3: Conclusion.
Required condition: \[ V^2 \ge \frac{rg}{\mu_s} \] Final Answer: Option (C)