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:

A particle moves in $$x$$-$$y$$ plane under the influence of a force $$\vec{F}$$ such that its linear momentum is $$\overrightarrow{\mathrm{p}}(\mathrm{t})=\hat{i} \cos (\mathrm{kt})-\hat{j} \sin (\mathrm{kt})$$. If $$\mathrm{k}$$ is constant, the angle between $$\overrightarrow{\mathrm{F}}$$ and $$\overrightarrow{\mathrm{p}}$$ will be :

A heavy box of mass $$50 \mathrm{~kg}$$ is moving on a horizontal surface. If co-efficient of kinetic friction between the box and horizontal surface is 0.3 then force of kinetic friction is :

A wooden block of mass $$5 \mathrm{~kg}$$ rests on a soft horizontal floor. When an iron cylinder of mass $$25 \mathrm{~kg}$$ is placed on the top of the block, the floor yields and the block and the cylinder together go down with an acceleration of $$0.1 \mathrm{~ms}^{-2}$$. The action force of the system on the floor is equal to :