A boy pushes a box of mass 2 kg with a force $$\overrightarrow F = \left( {20\widehat i + 10\widehat j} \right)N$$ on a frictionless surface. If the box was initially at rest, then ___________ m is displacement along the x-axis after 10s.

As shown in the figure, a block of mass $$\sqrt 3 $$ kg is kept on a horizontal rough surface of coefficient of friction $${1 \over {3\sqrt 3 }}$$. The critical force to be applied on the vertical surface as shown at an angle 60$$^\circ$$ with horizontal such that it does not move, will be 3x. The value of x will be _________.

[g = 10 m/s²; sin60$$^\circ$$ = $${{\sqrt 3 } \over 2}$$; cos60$$^\circ$$ = $${1 \over 2}$$]

An inclined plane is bent in such a way that the vertical cross-section is given by $$y = {{{x^2}} \over 4}$$ where y is in vertical and x in horizontal direction. If the upper surface of this curved plane is rough with coefficient of friction $$\mu$$ = 0.5, the maximum height in cm at which a stationary block will not slip downward is _________ cm.

The coefficient of static friction between a wooden block of mass 0.5 kg and a vertical rough wall is 0.2. The magnitude of horizontal force that should be applied on the block to keep it adhere to the wall will be _________ N. [g = 10 ms^$$-$$2]