$A$ circular overbridge has a radius of $20\,m$. What is the maximum speed with which a car can cross the bridge without leaving contact with the overbridge at the highest point (in $,m/s$)? $(g = 9.8\,m/s^2)$

$A$ particle of mass $m$ is suspended from a ceiling through a string of length $L$. The particle moves in a horizontal circle of radius $r$ such that $r = \frac{L}{\sqrt{2}}$. The speed of the particle will be:

The end $B$ of the rod $AB$ which makes an angle $\theta$ with the floor is being pulled with a constant velocity $v_0$ as shown. The length of the rod is $l$. At the instant when $\theta = 37^o$,then:

$A$ motorcycle driver doubles their velocity when taking a turn. The force exerted outwardly will be

One end of a string of length $l$ is connected to a particle of mass $m$ and the other end is connected to a small peg on a smooth horizontal table. If the particle moves in a circle with speed $v$,the net force on the particle (directed towards the center) will be ($T$ represents the tension in the string).

$A$ stick has its bottom end attached to a wall by a pivot and is held up by a massless string attached to its other end. Which of the following scenarios has the smallest tension in the string? (Length of stick is same in all scenarios)