A stone of mass $$2 \mathrm{~kg}$$ is hung from the ceiling of the room using two strings. If the strings make an angle $$60^{\circ}$$ and $$30^{\circ}$$ respectively with the horizontal surface of the roof then the tension on the longer string is : $$g=10 \mathrm{~ms}^{-2}$$

If the resultant of all external forces acting on a system of particles is zero, then from an inertial frame one can surely say that

$$\mathrm{F}_{\mathrm{A}}, \mathrm{F}_{\mathrm{B}}$$ and $$\mathrm{F}_{\mathrm{C}}$$ are three forces acting at point $$\mathrm{P}$$ as shown in figure. The whole system is in equilibrium state. The magnitude of $$\mathrm{F}_{\mathrm{A}}$$ is

A hockey player hits the ball at an angle of $$37^{\circ}$$ from the horizontal with an initial speed of $$40 \mathrm{~m} / \mathrm{s}$$ (a right angled triangle with one of the angle is $$37^{\circ}$$ and their sides in the ratio of $$6: 8: 10$$). Assume that the ball is in a vertical plane. The time at which the ball reaches the highest point of its path is