A small particle of mass m moving inside a heavy, hollow and straight tube along the tube axis undergoes elastic collision at two ends. The tube has no friction and it is closed at one end by a flat surface while the other end is fitted with a heavy movable flat piston as shown in figure.



When the distance of the piston from closed end is L = L₀, the particle speed is v = v₀. The piston is moved inward at a very low speed V such that $$V < < {{dL} \over L}{v_0}$$, where dL is the infinitesimal displacement of the piston. Which of the following statement(s) is/are correct?

A particle of mass $$m$$ is initially at rest at the origin. It is subjected to a force and starts moving along the $$x$$-axis. Its kinetic energy $$K$$ changes with time as $$dK/dt = \gamma t,$$ where $$\gamma $$ is a positive constant of appropriate dimensions. Which of a positive constant of appropriate dimensions. Which of the following statement is (are) true?

A flat plate is moving normal to its plane through a gas under the reaction of a constant force $$F.$$ The gas is kept at a very low pressure. The speed of the plate $$v$$ is much less than the average speed u of the gas molecules.

Which of the following options is /are true?

A thin ring of mass 2 kg and radius 0.5 m is rolling without on a horizontal plane with velocity 1 m/s. A small ball of mass 0.1 kg, moving with velocity 20 m/s in the opposite direction hits the ring at a height of 0.75 m and goes vertically up with velocity 10 m/s. Immediately after the collision,