A solid cylinder and a solid sphere, having same mass $$M$$ and radius $$R$$, roll down the same inclined plane from top without slipping. They start from rest. The ratio of velocity of the solid cylinder to that of the solid sphere, with which they reach the ground, will be :

Three identical particles $$\mathrm{A}, \mathrm{B}$$ and $$\mathrm{C}$$ of mass $$100 \mathrm{~kg}$$ each are placed in a straight line with $$\mathrm{AB}=\mathrm{BC}=13 \mathrm{~m}$$. The gravitational force on a fourth particle $$\mathrm{P}$$ of the same mass is $$\mathrm{F}$$, when placed at a distance $$13 \mathrm{~m}$$ from the particle $$\mathrm{B}$$ on the perpendicular bisector of the line $$\mathrm{AC}$$. The value of $$\mathrm{F}$$ will be approximately :

A certain amount of gas of volume $$\mathrm{V}$$ at $$27^{\circ} \mathrm{C}$$ temperature and pressure $$2 \times 10^{7} \mathrm{Nm}^{-2}$$ expands isothermally until its volume gets doubled. Later it expands adiabatically until its volume gets redoubled. The final pressure of the gas will be (Use $$\gamma=1.5)$$ :

Following statements are given :

(A) The average kinetic energy of a gas molecule decreases when the temperature is reduced.

(B) The average kinetic energy of a gas molecule increases with increase in pressure at constant temperature.

(C) The average kinetic energy of a gas molecule decreases with increase in volume.

(D) Pressure of a gas increases with increase in temperature at constant pressure.

(E) The volume of gas decreases with increase in temperature.

Choose the correct answer from the options given below :