Roads are banked on curves so that
The speeding vehicles may not fall outwards
The frictional force between the road and vehicle may be decreased
The wear and tear of tyres may be avoided
The weight of the vehicle may be decreased
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 ball of mass $0.5 \mathrm{~kg}$ is attached to a string of length $50 \mathrm{~cm}$. The ball is rotated on a horizontal circular path about its vertical axis. The maximum tension that the string can bear is $400 \mathrm{~N}$. The maximum possible value of angular velocity of the ball in rad/s is,:
A particle moves in a circle of radius $25\,cm$ at two revolutions per sec. The acceleration of the particle in $m/s^2$ is
The driver of a car travelling at velocity $v$ suddenly see a broad wall in front of him at a distance $d$. He should
The centripetal acceleration is given by