A $$1 \mathrm{~kg}$$ mass is suspended from the ceiling by a rope of length $$4 \mathrm{~m}$$. A horizontal force '$$F$$' is applied at the mid point of the rope so that the rope makes an angle of $$45^{\circ}$$ with respect to the vertical axis as shown in figure. The magnitude of $$F$$ is :

(Assume that the system is in equilibrium and $$g=10 \mathrm{~m} / \mathrm{s}^2$$)

A heavy iron bar, of weight $$W$$ is having its one end on the ground and the other on the shoulder of a person. The bar makes an angle $$\theta$$ with the horizontal. The weight experienced by the person is :

A light unstretchable string passing over a smooth light pulley connects two blocks of masses $$m_1$$ and $$m_2$$. If the acceleration of the system is $$\frac{g}{8}$$, then the ratio of the masses $$\frac{m_2}{m_1}$$ is :

A given object takes $$\mathrm{n}$$ times the time to slide down $$45^{\circ}$$ rough inclined plane as it takes the time to slide down an identical perfectly smooth $$45^{\circ}$$ inclined plane. The coefficient of kinetic friction between the object and the surface of inclined plane is :