Imagine that a reactor converts all given mass into energy and that it operates at a power level of 109 watt. The mass of the fuel consumed per hour in the reactor will be : (velocity of light, c is 3×108 m/s)

The acceleration of an electron in the first orbit of the hydrogen atom (n = 1) is :

According to Bohr’s theory, the time averaged magnetic field at the centre (i.e. nucleus) of a hydrogen atom due to the motion of electrons in the nth orbit is proportional to : (n = principal quantum number)

A radioactive nucleus A with a half life T, decays into a nucleus B. At t = 0, there is no nucleus B. At sometime t, the ratio of the number of B to that of A is 0.3. Then, t is given by :

Some energy levels of a molecule are shown in the figure. The ratio of the wavelengths r = $${\lambda }_1$$/$${\lambda }_2$$, is given by:

CP and Cv are specific heats at constant pressure and constant volume respectively. It is observed that CP – Cv = a for hydrogen gas CP – Cv = b for nitrogen gas The correct relation between a and b is

A copper ball of mass 100 gm is at a temperature T. It is dropped in a copper calorimeter of mass 100 gm, filled with 170 gm of water at room temperature. Subsequently, the temperature of the system is found to be 75oC. T is given by: (Given : room temperature = 30oC, specific heat of copper = 0.1 cal/gmoC)

An external pressure P is applied on a cube at 0oC so that it is equally compressed from all sides. K is the bulk modulus of the material of the cube and $$\alpha$$ is its coefficient of linear expansion. Suppose we want to bring the cube to its original size by heating. The temperature should be raised by:

The temperature of an open room of volume 30 m3 increases from 17oC to 27oC due to the sunshine. The atmospheric pressure in the room remains 1 $$\times$$ 105 Pa. If Ni and Nf are the number of molecules in the room before and after heating, then Nf – Ni will be :

In an experiment, a sphere of aluminium of mass 0.20 kg is heated upto 150oC. Immediately, it is put into water of volume 150 cc at 27oC kept in a calorimeter of water equivalent to 0.025 kg. Final temperature of the system is 40oC. The specific heat of aluminium is : (take 4.2 Joule = 1 calorie)

A compressive force, F is applied at the two ends of a long thin steel rod. It is heated, simultaneously, such that its temperature increases by $$\Delta$$T. The net change in its length is zero. Let $$\ell$$ be the length of the rod, A its area of cross-section,Y its Young’s modulus, and $$\alpha$$ its coefficient of linear expansion. Then, F is equal to :

An engine operates by taking n moles of an ideal gas through the cycle ABCDA shown in figure. The thermal efficiency of the engine is : (Take Cv = 1.5 R, where R is gas constant)

An ideal gas has molecules with 5 degrees of freedom. The ratio of specific heats at constant pressure (Cp ) and at constant volume (Cv) is :

A steel rail of length 5 m and area of cross section 40cm2 is prevented from expanding along its length while the temperature rises by 10oC. If coefficient of linear expansion and Young’s modulus of steel are 1.2×10−5 K−1 and 2×1011 Nm−2 respectively, the force developed in the rail is approximately :

N moles of a diatomic gas in a cylinder are at a temperature T. Heat is supplied to the cylinder such that the temperature remains constant but n moles of the diatomic gas get converted into monoatomic gas. What is the change in the total kinetic energy of the gas ?

For the P-V diagram given for an ideal gas, out of the following which one correctly represents the T-P diagram ?

An electric dipole has a fixed dipole moment $$\overrightarrow{p}$$, which makes angle $$\theta$$ with respect to x-axis. When subjected to an electric field $$\overrightarrow{E_1}=E\hat{i}$$ , it experiences a torque $$\overrightarrow{T_1}=\tau \hat{k}$$ . When subjected to another electric field $$\overrightarrow{E_2}=\sqrt{3}{E}_1\hat{j}$$ it experiences a torque $$\overrightarrow{T_2}=\overrightarrow{-T_1}$$ . The angle $$\theta$$ is:

Four closed surfaces and corresponding charge distributions are shown below. Let the respective electric fluxes through the surfaces be $${\Phi }_1,$$ $${\Phi }_2,$$ $${\Phi }_3$$ and $${\Phi }_4$$. Then :

There is a uniform electrostatic field in a region. The potential at various points on a small sphere centred at $$P,$$ in the region, is found to vary between the limits 589.0 V to 589.8 V. What is the potential at a point on the sphere whose radius vector makes an angle of 60o with the direction of the field ?

A body is thrown vertically upwards. Which one of the following graphs correctly represent the velocity vs time?