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 :

A player caught a cricket ball of mass $$150 \mathrm{~g}$$ moving at a speed of $$20 \mathrm{~m} / \mathrm{s}$$. If the catching process is completed in $$0.1 \mathrm{~s}$$, the magnitude of force exerted by the ball on the hand of the player is:

A body of weight $$200 \mathrm{~N}$$ is suspended from a tree branch through a chain of mass $$10 \mathrm{~kg}$$. The branch pulls the chain by a force equal to (if $$\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$$) :

A light string passing over a smooth light pulley connects two blocks of masses $$m_1$$ and $$m_2\left(\right.$$ where $$\left.m_2>m_1\right)$$. If the acceleration of the system is $$\frac{g}{\sqrt{2}}$$, then the ratio of the masses $$\frac{m_1}{m_2}$$ is: