Two masses $$M_1$$ and $$M_2$$ are arranged as shown in the figure. Let $$a$$ be the magnitude of the acceleration of the mass $$M_1$$. If the mass of $$M_1$$ is doubled and that of $$M_2$$ is halved, then the acceleration of the system is (Treat all surfaces as smooth; masses of pulley and rope are negligible)

Two rectangular blocks of masses 40 kg and 60 kg are connected by a string and kept on a frictionless horizontal table. If a force of 1000 N is applied on 60 kg block away from 40 kg block, then the tension in string is

A book is lying on a table. What is the angle between the normal reaction acting on the book on the table and the weight of the book?

Two blocks $$A$$ and $$B$$ of masses $$4 \mathrm{~kg}$$ and $$6 \mathrm{~kg}$$ are as shown in the figure. A horizontal force of $$12 \mathrm{~N}$$ is required to make $$A$$ slip over $$B$$. Find the maximum horizontal force $$F_B$$ that can be applied on $B$, so that both $$A$$ and $$B$$ move together (take, $$g=10 \mathrm{~ms}^{-2}$$ )