A motorcyclist rides in a horizontal circle a | vedclass

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(D) For a motorcyclist moving in a horizontal circle inside a cylindrical wall,the forces acting on the motorcyclist are:$1$. The weight $(mg)$ acting

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$\sqrt{\frac{r g}{\mu}}$

Vedclass · Answer

(D) For a motorcyclist moving in a horizontal circle inside a cylindrical wall,the forces acting on the motorcyclist are:$1$. The weight $(mg)$ acting downwards.$2$. The normal force $(N)$ acting horizontally towards the center,which provides the necessary centripetal force: $N = \frac{mv^2}{r}$.$3$. The frictional force $(f)$ acting upwards,which balances the weight to prevent skidding: $f = mg$.For the motorcyclist not to skid,the frictional force must be less than or equal to the limiting friction: $f \le \mu N$.Substituting the values: $mg \le \mu \left(\frac{mv^2}{r}\right)$.$g \le \frac{\mu v^2}{r}$.$v^2 \ge \frac{rg}{\mu}$.Therefore,the minimum speed is $v_{min} = \sqrt{\frac{rg}{\mu}}$.

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