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)$$^{-1}$$ |
Column I gives certain situations in which a straight metallic wire of resistance R is used and Column II gives some resulting effects. Match the statements in Column I with the statements 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) | A charged capacitor is connected to the ends of the wire | (P) | A constant current flows through the wire |
| (B) | The wire is moved perpendicular to its length with a constant velocity in a uniform magnetic field perpendicular to the plane of motion | (Q) | Thermal energy is generated in the wire |
| (C) | The wire is placed in a constant electric field that has a direction along the length of the wire. | (R) | A constant potential difference develops between the ends of the wire |
| (D) | A battery of constant emf is connected to the ends of the wire | (S) | Charges of constant magnitude appear at the ends of the wire |
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