Two identical blocks each of mass ' M ' attached to the ends of a massless inextensible string which passes over a pulley with a fixed axis as shown below. A small mass ' $m$ ' is now placed on the block B. The acceleration with which the two blocks move together is [g = gravitational acceleration]

A machine gun fires bullets of mass $$30 \mathrm{~g}$$ with velocity of $$1000 \mathrm{~m} / \mathrm{s}$$. The man holding the gun can exert a maximum force of $$300 \mathrm{~N}$$ on it. How many bullets can he fire per second at most?

A spring balance is attached to the ceiling of a lift. A man hangs his bag on the spring and the spring balance reads $$49 \mathrm{~N}$$, when the lift is stationary. If the lift moves downward with an acceleration of $$5 \mathrm{~m} / \mathrm{s}^2$$, the reading of the spring balance will be $$\left(g=9.8 \mathrm{~m} / \mathrm{s}^2\right)$$

A door $$1.2 \mathrm{~m}$$ wide requires a force of $$1 \mathrm{~N}$$ to be applied perpendicular at the free end to open or close it. The perpendicular force required at a point $$0.2 \mathrm{~m}$$ distant from the hinges for opening or closing the door is