A man standing on the roof of a house of height $h$ throws one particle vertically downwards and another particle horizontally with the same velocity $u$. The ratio of their velocities when they reach the earth's surface will be
$\sqrt {2gh + {u^2}} :u$
$1:2$
$1:1$
$\sqrt {2gh + {u^2}} :\sqrt {2gh} $
The linear speed of the tip of seconds hand of a wall clock is $1.05\,cm\,s^{-1}.$ The length of the seconds hand is nearly ........ $cm$
Three point particles $P, Q, R$ move in circle of radius $‘r’$ with different but constant speeds. They start moving at $t = 0$ from their initial positions as shown in the figure. The angular velocities (in rad/ sec) of $P, Q$ and $R$ are $5\pi , 2\pi$ & $3\pi$ respectively, in the same sense. the number of times $P$ and $Q$ meet in that time interval is:
A ring of mass $m$ moves from point $1$ to point $2$ along a smooth rigid horizontal wire with a constant speed $v$. The average force acting the ring over the time of its motion from $1$ to $2$ is
A smooth wire of length $2\pi r$ is bent into a circle and kept in a vertical plane. A bead can slide smoothly on the wire. When the circle is rotating with angular speed $\omega$ about the vertical diameter $AB$, as shown in figure, the bead is at rest with respect to the circular ring at position $P$ as shown. Then the value of $\omega^2$ is equal to
A particle of mass $m$ describes a circle of radius $r$. The centripetal acceleration of the particle is $4/r^2$. What will be the momentum of the particle?