Consider two ideal diatomic gases A and B at some temperature T. Molecules of the gas A are rigid, and have a mass m. Molecules of the gas B have an additional vibrational mode, and have a mass {m \over 4} . The ratio of the specific heats ($$C_V^A$$ and $$C_V^B$$ ) of gas A and B, respectively is :

When the temperature of a metal wire is increased from 0oC to 10oC, its length increases by 0.02%. The percentage change in its mass density will be closest to :

A gas mixture consists of 3 moles of oxygen and 5 moles of argon at temperature T. Assuming the gases to be ideal and the oxygen bond to be rigid, the total internal energy (in units of RT) of the mixture is :

Match the {{{C_P}} \over {{C_V}}} ratio for ideal gases with different type of molecules : .tg {border-collapse:collapse;border-spacing:0;} .tg td{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px; overflow:hidden;padding:10px 5px;word-break:normal;} .tg th{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px; font-weight:normal;overflow:hidden;padding:10px 5px;word-break:normal;} .tg .tg-baqh{text-align:center;vertical-align:top} .tg .tg-0lax{text-align:left;vertical-align:top} Molecule Type CP/CV (A) Monatomic (I) 7/5 (B) Diatomic rigid molecules (II) 9/7 (C) Diatomic non-rigid molecules (III) 4/3 (D) Triatomic rigid molecules (IV) 5/3

Which of the following is an equivalent cyclic process corresponding to the thermodynamic cyclic given in the figure ? where, 1 $$\to$$ 2 is adiabatic. (Graphs are schematic and are not to scale)

The specific heat of water = 4200 J kg-1K-1 and the latent heat of ice = 3.4 $$\times$$ 105 J kg–1. 100 grams of ice at 0oC is placed in 200 g of water at 25oC. The amount of ice that will melt as the temperature of water reaches 0oC is close to (in grams) :

Two gases-argon (atomic radius 0.07 nm, atomic weight 40) and xenon (atomic radius 0.1 nm, atomic weight 140) have the same number density and are at the same temperature. The raito of their respective mean free times is closest to :

Consider a sphere of radius R which carries a uniform charge density $$\rho$$. If a sphere of radius {{R \over 2}} is carved out of it, as shown, the ratio {{\left| {\overrightarrow {{E_A}} } \right|} \over {\left| {\overrightarrow {{E_B}} } \right|}} of magnitude of electric field $$\overrightarrow{E_A}$$ and $$\overrightarrow{E_B}$$, respectively, at points A and B due to the remaining portion is :

Consider the force F on a charge 'q' due to a uniformly charged spherical shell of radius R carrying charge Q distributed uniformly over it. Which one of the following statements is true for F, if 'q' is placed at distance r from the centre of the shell?

Two identical electric point dipoles have dipole moments $${\overrightarrow{p}}_1=p\hat{i}$$ and $${\overrightarrow{p}}_2=-p\hat{i}$$ and are held on the x axis at distance '$$a$$' from each other. When released, they move along the x-axis with the direction of their dipole moments remaining unchanged. If the mass of each dipole is 'm', their speed when they are infinitely far apart is :

Charges Q1 and Q2 are at points A and B of a right angle triangle OAB (see figure). The resultant electric field at point O is perpendicular to the hypotenuse, then {{{Q_1}} \over {{Q_2}}} is proportional to :

Ten charges are placed on the circumference of a circle of radius R with constant angular separation between successive charges. Alternate charges 1, 3, 5, 7, 9 have charge (+q) each, while 2, 4, 6, 8, 10 have charge (–q) each. The potential V and the electric field E at the centre of the circle are respectively. (Take V = 0 at infinity)

A solid sphere of radius R carries a charge Q + q distributed uniformly over its volume. A very small point like piece of it of mass m gets detached from the bottom of the sphere and falls down vertically under gravity. This piece carries charge q. If it acquires a speed v when it has fallen through a vertical height y (see figure), then : (assume the remaining portion to be spherical).

A particle of charge q and mass m is subjected to an electric field E = E0 (1 – $$a$$x2) in the x-direction, where $$a$$ and E0 are constants. Initially the particle was at rest at x = 0. Other than the initial position the kinetic energy of the particle becomes zero when the distance of the particle from the origin is :

Concentric metallic hollow spheres of radii R and 4R hold charges Q1 and Q2 respectively. Given that surface charge densities of the concentric spheres are equal, the potential difference V(R) – V(4R) is :

Two isolated conducting spheres S1 and S2 of radius {2 \over 3}R and {1 \over 3}R have 12 $$\mu$$C and –3 $$\mu$$C charges, respectively, and are at a large distance from each other. They are now connected by a conducting wire. A long time after this is done the charges on S1 and S2 are respectively :

A charge Q is distributed over two concentric conducting thin spherical shells radii r and R (R > r). If the surface charge densities on the two shells are equal, the electric potential at the common centre is :

A small point mass carrying some positive charge on it, is released from the edge of a table. There is a uniform electric field in this region in the horizontal direction. Which of the following options then correctly describe the trajectory of the mass? (Curves are drawn schematically and are not to scale).

A charged particle (mass m and charge q) moves along X-axis with velocity V0. When it passes through the origin it enters a region having uniform electric field $$\overrightarrow{E}=-E\hat{j}$$ which extends upto x = d. Equation of path of electron in the region x > d is

A two point charges 4q and -q are fixed on the x-axis at x = - {d \over 2} and x = {d \over 2} respectively. If a third point charge 'q' is taken from the origin to x = d along the semicircle as shown in the figure, the energy of the charge will :