Is the maximum safe speed of a vehicle on a banked curved road higher or lower than on a flat curved road?

$A$ particle on the inner rough surface of a cone rotating about its vertical axis is at rest relative to the cone at a height of $1 \ m$ above its vertex. If the coefficient of friction is $\mu = 0.5$ and the semi-vertical angle of the cone is $45^\circ$,what is the maximum angular velocity $\omega$ of the cone?

$A$ car of mass $1500 \ kg$ is moving with a speed of $12.5 \ m/s$ on a circular path of radius $20 \ m$ on a level road. What should be the coefficient of friction between the car and the road,so that the car does not slip?

$A$ particle is moving along the circle $x^2 + y^2 = a^2$ in an anticlockwise direction. The $x-y$ plane is a rough horizontal stationary surface. At the point $(a \cos \theta, a \sin \theta)$,the unit vector in the direction of friction on the particle is:

$A$ plank is resting on a horizontal ground in the northern hemisphere of the earth at a $45^{\circ}$ latitude. Let the angular speed of the earth be $\omega$ and its radius $r_e$. The magnitude of the frictional force on the plank will be

If a cyclist moving with a speed of $4.9 \, m/s$ on a level road can take a sharp circular turn of radius $4 \, m$,then the coefficient of friction between the cycle tyres and the road is: