If a car is moving on banked road of radius $300 \mathrm{m}$ and angle of banking $30°$, then find the safe speed of the car. Take $g=10 \mathrm{m} {\mathrm{s}}^{-2}$.

Statement I: A cyclist is moving on an unbanked road with a speed of $7 \mathrm{km} {\mathrm{h}}^{-1}$ and takes a sharp circular turn along a path of the radius of $2 \mathrm{m}$ without reducing the speed. The static friction coefficient is $0.2$. The cyclist will not slip and pass the curve $\left(g=9.8 \mathrm{m} {\mathrm{s}}^{-2}\right)$

Statement II : If the road is banked at an angle of $45°$, cyclist can cross the curve of $2 \mathrm{m}$ radius with the speed of $18.5 \mathrm{km} {\mathrm{h}}^{-1}$ without slipping. In the light of the above statements, choose the correct answer from the options given below.

A modern grand-prix racing car of mass $m$ is travelling on a flat track in a circular arc of radius $R$ with a speed $v.$ If the coefficient of static friction between the tyres and the track is ${\mu }_{\mathrm{s}},$ then the magnitude of negative lift $F_L$ acting downwards on the car is:

An unbanked curve has a radius of $60 \mathrm{m}$. The maximum speed at which the car make a turn is (Take $\mu =0.75$)

A coin, placed on a rotating turntable at a distance of $8 \text{cm}$ from the centre, slips. If the angular velocity of the turntable is doubled, it will just slip at a distance of

A body moves along a circular path of radius $5 \mathrm{m}$. The coefficient of friction between the surface of path and the body is $0.5$. The angular velocity, in $\mathrm{rad} {\mathrm{s}}^{-1}$, with which the body should move so that it does not leave the path is $(g=10 \mathrm{m}{\mathrm{s}}^{-2})$