Explain the reason behind the bending of cyclist on a horizontal road while taking a turn.

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:

Represent the union of two sets by Venn diagram for each of the following.

$X=\{x | x$ is a prime number between $80$ and $100\}$

$Y=\{y | y$ is an odd number between $90$ and $100\}$

A cyclist rides along the circumference of a circular horizontal plane of radius $R$, the friction coefficient being dependent only on distance $r$ from the centre $O$ of the plane as $k=k_0\left(1-\frac{r}{R}\right)$, where $k_0$ is a constant. What is the cyclist's maximum velocity with the centre at the point along which the cyclist can ride?

A railway carriage has its centre of gravity at a height of $1 \mathrm{m}$ above the rails, which are $1.5 \mathrm{m}$ apart. The maximum safe speed at which it could travel round an unbanked curve of radius $100 \mathrm{m}$ is