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,

A force $$F = - K\left( {y\widehat i + x\widehat j} \right)$$ (where K is a positive constant) acts on a particle moving in the xy plane. Starting from the origin, the particle is taken along the positive x axis to the point $$\left( {a,0} \right)$$, and then parallel to the y axis to the point $$\left( {a,a} \right)$$. The total work done by the force F on the particle is