$A$ car is moving on an overbridge of radius $R$ with a constant speed $v$. As the car is descending on the overbridge from point $B$ to $C$,the normal reaction on it due to the bridge:

When a disc is rotating with angular velocity $\omega$,a particle situated at a distance of $4 \ cm$ just begins to slip. If the angular velocity is doubled,at what distance will the particle start to slip (in $cm$)?

$A$ particle describes a horizontal circle in a conical funnel whose inner surface is smooth with a speed of $0.5 \, m/s$. What is the height of the plane of the circle from the vertex of the funnel in $cm$?

$A$ particle is released on a vertical smooth semicircular track from point $X$ so that $OX$ makes an angle $\theta$ from the vertical (see figure). The normal reaction of the track on the particle vanishes at point $Y$ where $OY$ makes an angle $\phi$ with the horizontal. Then

$A$ particle of mass $M$ moves with constant speed along a circular path of radius $r$ under the action of a force $F$. Its speed is

$A$ car travelling on a smooth road passes through a curved portion of the road in the form of an arc of a circle of radius $10 \, m$. If the mass of the car is $500 \, kg$,the reaction on the car at the lowest point $P$ where its speed is $20 \, m/s$ is ......... $kN$.