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 u, is the coefficient of static friction between the wheels of vehicle and walls then correct relation is ______.

[g = acceleration due to gravity]

Options

• `V^2 le (rg)/mu_s`

• `V le (rg)/mu_s`

• `V^2 ge (rg)/mu_s`

• `V ge (rg)/mu_s`

Answer 1

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 u, is the coefficient of static friction between the wheels of vehicle and walls then correct relation is `bbunderline(V^2 ge (rg)/mu_s)`.

Explanation:

In the “well of death”, the centripetal force is provided by the normal reaction (N):

N = `(mV^2)/r`

The friction force balances the weight:

f = μ_s​N ≥ mg

`mu_s * (mV^2)/r` ≥ mg

V² ≥ `(rg)/mu_s`