$A$ 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:

Find the centripetal force acting on a coin weighing $0.1 \,kg$ placed $0.1 \,m$ from the centre on a gramophone disc rotating at $600 \,rpm$.

The $x$ and $y$ displacements of a particle are given as $x(t) = a \sin \omega t$ and $y(t) = a \sin 2 \omega t$. Its trajectory will look like:

$A$ mass of $100\, g$ is tied to one end of a string $2\, m$ long. The body is revolving in a horizontal circle making a maximum of $200$ revolutions per minute. The other end of the string is fixed at the center of the circle of revolution. The maximum tension that the string can bear is .......... $N$ (approximately).

$A$ car is moving with velocity $v$ at the top of a semi-circular hill of radius $40 \,m$ such that the normal force on it is zero. Find the velocity $(v)$ of the car. [Use $g=10 \,ms^{-2}$] (in $\,ms^{-1}$)

$A$ motorcycle is moving on an overbridge of radius $R$. The driver maintains a constant speed $v$. As the motorcycle is ascending on the overbridge,the normal force on it