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 :

From a solid sphere of mass $$M$$ and radius $$R$$ a cube of maximum possible volume is cut. Moment of inertia of cube about an axis passing through its center and perpendicular to one of its face is:

Distance of the center of mass of a solid uniform cone from its vertex is $$z{}_0$$. If the radius of its base is $$R$$ and its height is $$h$$ then $$z{}_0$$ is equal to :

A particle of mass $$m$$ moving in the $$x$$ direction with speed $$2v$$ is hit by another particle of mass $$2m$$ moving in the $$y$$ direction with speed $$v.$$ If the collision is perfectly inelastic, the percentage loss in the energy during the collision is close to: