The angular speed of earth around its own axis is ......... $rad / s$

A small block is shot into each of the four tracks as shown below. Each of the tracks rises to the same height. The speed with which the block enters the track is the same in all cases. At the highest point of the track, the normal reaction is maximum in

A particle is moving in $x y$-plane in a circular path with centre at origin. If at an instant the position of particle is given by $\frac{1}{\sqrt{2}}(\hat{i}+\hat{j})$, then velocity of particle is along .......

A boy ties a stone of mass $100 \,g$ to the end of a $2$ $m$ long string and whirls it around in a horizontal plane. The string can withstand the maximum tension of $80 \,N$. If the maximum speed with which the stone can revolve is $\frac{ K }{\pi} rev$. / $min$. The value of $K$ is (Assume the string is massless and unstretchable)

particle is moving in a circular path. The acceleration and momentum of the particle at a certain moment are $\vec a\, = \,(4\hat i + 3\hat j)\,\,m/{s^2}$ and $\vec P\, = \,(8\hat i\, - \,6\hat j)\,kg\, - \,m/s$ . The motion of the particle is

The kinetic energy $k$ of a particle moving along a circle of radius $R$ depends on the distance covered $s$ as $k = as^2$ where $a$ is a constant. The force acting on the particle is