A particle of mass $200 \,g$ is moving in a circle of radius $2 \,m$. The particle is just 'looping the loop'. The speed of the particle and the tension in the string at highest point of the circular path are $\left(g=10 \,ms ^{-2}\right)$

A particle moves in a circular path with decreasing speed. Choose the correct statement.

The driver of a car travelling at velocity $v$ suddenly see a broad wall in front of him at a distance $d$. He should

Roads are banked on curves so that

A particle $P$ is sliding down a frictionless hemispherical bowl. It passes the point $A$ at $t = 0$. At this instant of time, the horizontal component of its velocity is $v$. A bead $Q$ of the same mass as $P$ is ejected from $A$ at $t = 0$ along the horizontal string $AB$ (see figure) with the speed $v$. Friction between the bead and the string may be neglected. Let ${t_P}$ and ${t_Q}$ be the respective time taken by $P$ and $Q$ to reach the point $B$. Then

A particle is moving with constant speed $v$ in $x y$ plane as shown in figure. The magnitude of its angular velocity about point $O$ is .........