Given in the figure are two blocks $$A$$ and $$B$$ of weight 20 N and 100 N, respectively. These are being pressed against a wall by a force $$F$$ as shown. If the coefficient of friction between the blocks is 0.1 and between block $$B$$ and the wall is 0.15, the frictional force applied by the wall on block $$B$$ is :

A block of mass $$m$$ is placed on a surface with a vertical cross section given by $$y = {{{x^3}} \over 6}.$$ If the coefficient of friction is $$0.5,$$ the maximum height above the ground at which the block can be placed without slipping is:

A particle of mass $$m$$ is at rest at the origin at time $$t=0.$$ It is subjected to a force $$F\left( t \right) = {F_0}{e^{ - bt}}$$ in the $$x$$ direction. Its speed $$v(t)$$ is depicted by which of the following curves?

Two fixed frictionless inclined planes making an angle $${30^ \circ }$$ and $${60^ \circ }$$ with the vertical are shown in the figure. Two blocks $$A$$ and $$B$$ are placed on the two planes. What is the relative vertical acceleration of $$A$$ with respect to $$B$$ ?