A fixed thermally conducting cylinder has a radius $R$ and height $L_0$. The cylinder is open at its bottom and has a small hole at its top. A piston of mass $M$ is held at a distance $L$ from the top surface, as shown in the figure. The atmospheric pressure is $P_0$.
The piston is now pulled out slowly and held at a distance 2L from the top. The pressure in the cylinder between its top and the piston will then be
A fixed thermally conducting cylinder has a radius $R$ and height $L_0$. The cylinder is open at its bottom and has a small hole at its top. A piston of mass $M$ is held at a distance $L$ from the top surface, as shown in the figure. The atmospheric pressure is $P_0$.
While the piston is at a distance 2L from the top, the hole at the top is sealed. The piston is then released, to a position where it can stay in equilibrium. In this condition, the distance of the piston from the top is :
A fixed thermally conducting cylinder has a radius $R$ and height $L_0$. The cylinder is open at its bottom and has a small hole at its top. A piston of mass $M$ is held at a distance $L$ from the top surface, as shown in the figure. The atmospheric pressure is $P_0$.
The piston is taken completely out of the cylinder. The hole at the top is sealed. A water tank is brought below the cylinder and put in a position so that the water surface in the tank is at the same level as the top of the cylinder as shown in the figure. The density of the water is $$\rho$$. In equilibrium, the height H of the water column in the cylinder satisfies
Some physical quantities are given in Column I and some possible SI units in which these quantities may be expressed are given in Column II. Match the physical quantities in Column I with the units in Column II and indicate your answer by darkening appropriate bubbles in the 4 $$\times$$ 4 matrix given in the ORS.
| Column I | Column II | ||
|---|---|---|---|
| (A) | GM$$_e$$M$$_s$$ G - universal gravitational constant, M$$_e$$ - mass of the earth, M$$_s$$ - mass of the Sun |
(P) | (volt) (coulomb) (metre) |
| (B) | $${{3RT} \over M}$$ R - universal gas constant, T - absolute temperature, M - molar mass |
(Q) | (kilogram) (metre)$$^3$$ (second)$$^{-2}$$ |
| (C) | $${{{F^2}} \over {{q^2}{B^2}}}$$ F - force, q - charge, B - magnetic field |
(R) | (metre)$$^2$$ (second)$$^{-2}$$ |
| (D) | $${{G{M_e}} \over {{R_e}}}$$ G - universal gravitational constant, M$$_e$$ - mass of the earth R$$_e$$ - radius of the earth |
(S) | (farad) (volt)$$^2$$ (kg)$$^{-1}$$ |
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