A Particle of unit mass is moving on a plane. Its trajectory, in polar coordinates, is given by $$r\left( t \right) = {t^2},\theta \left( t \right) = t,$$ where $$t$$ is time. The kinetic energy of the particle at time $$t=2$$ is

The following figure shows the velocity- time plot for a particle traveling along a straight line. The distance covered by the particle from $$t = 0$$ to $$t= 5$$ $$s$$ is __________$$m.$$

A rigid ball of weight $$100$$ $$N$$ is suspended with the help of a string. The ball is pulled by a horizontal force $$F$$ such that the string makes an angle of $${30^0}$$ with the vertical. The magnitude of force $$F$$ (in N) is __________

A point mass $$M$$ is released from rest and slides down a spherical bowl (of radius $$R$$) from a height $$H$$ as shown in the figure below. The surface of the bowl is smooth (no friction). The velocity of the mass at the bottom of the bowl is