A cyclist speeding at 6ms^(-1) in a circle of 18 m radius makes an ang

A solid cylinder is rolling down on an inclined plane of angle $θ$ . The minimum value of the coefficient of friction between the plane and the cylinder to allow pure rolling
A $\frac{1}{3} tan θ$
B $\frac{2}{3} tan θ$
C $\frac{2}{5} tan θ$
D $\frac{4}{5} tan θ$
What is the minimum stopping distance for a vehicle of mass m moving with speed v along a level road. If the coefficient of friction between the tyres and the road is $μ$
A $\frac{v^{2}}{2 μ g}$
B $\frac{2 v^{2}}{μ g}$
C $\frac{v^{2}}{μ g}$
Dnone of these
In the given system, a block of mass m is resting on a board which makes an angle $θ$ with the horizontal. What should be the minimum value of $θ$ , so that the block just starts moving downwards? The coefficient of friction between the surfaces of the board and the block is $μ$ .

A ${tan}^{- 1} (1 / μ)$
B ${tan}^{- 1} (μ)$
C ${sin}^{- 1} μ$
Dnone

A cyclist speeding at $6 m s^{- 1}$ in a circle of 18 m radius makes an angle $θ$ with the vertical. Calculate $θ$ . Also determine the minimum possible value of the coefficient of friction between the tyres and the ground?