Question Bank Directory

A mass falls from a height $h$ and its time of fall $t$ is recorded in terms of time period $T$ of a simple pendulum. On the surface of the earth, it is found that $t=2T$. The entire setup is taken on the surface of another planet whose mass is half of that of the Earth and whose radius is the same. The same experiment is repeated and corresponding times are noted as $t'$ and $T'$. Then we can say:

The average kinetic energy of a helium atom at 30°C is:

Infinite number of bodies, each of mass 2 kg are situated on x-axis at distance 1m, 2m, 4m, 8m, respectively from the origin. The resulting gravitational potential due to this system at the origin will be:

A container of volume $200 \text{ cm}^3$ contains 0.2 mole of hydrogen gas and 0.3 mole of argon gas. The pressure of the system at temperature $200 \text{ K}$ ($R = 8.3 \text{ J K}^{-1} \text{ mol}^{-1}$) will be:

Orbital having 3 angular nodes and 3 total nodes is:

A remote sensing satellite of the earth revolves in a circular orbit at a height of $0.25 \times 10^6$ m above the surface of the earth. If the earth’s radius is $6.38 \times 10^6$ m and $g = 9.8$ ms$^{-2}$, then the orbital speed of the satellite is:

The pressure and temperature of two different gases are P and T with volume V for each. If they are mixed, keeping the same volume and temperature, the pressure of the mixture will be:

At what temperature will the rms speed of oxygen molecules become just sufficient for escaping from the earth's atmosphere? (Given: Mass of oxygen molecule $m = 2.76 \times 10^{-26} \text{ kg}$, Boltzmann's constant $k_B = 1.38 \times 10^{-23} \text{ J K}^{-1}$)

If $C_p$ and $C_v$ denote the specific heats (per unit mass) of an ideal gas of molecular weight $M$, then:

A given sample of an ideal gas occupies a volume $V$ at a pressure $p$ and absolute temperature $T$. The mass of each molecule of the gas is $m$. Which of the following gives the density of the gas?

Two vessels separately contain two ideal gases A and B at the same temperature, the pressure of A being twice that of B. Under such conditions, the density of A is found to be 1.5 times the density of B. The ratio of molecular weight of A and B is:

Electromagnets are made of soft iron because soft iron has:

For a gas, $R/C_V = 0.67$. This gas is made up of molecules which are:

A gas mixture consists of 2 moles of $O_2$ and 4 moles of Ar at temperature T. Neglecting all vibrational modes, the total internal energy of the system is:

Dependence of intensity of gravitational field (E) of earth with distance (r) from centre of earth is correctly represented by:

A particle of mass M is situated at the centre of a spherical shell of mass M and radius a. The gravitational potential at a point situated at a/2 distance from the centre will be:

The average thermal energy for a mono-atomic gas is: ($k_B$ is Boltzmann constant and $T$ absolute temperature)

Which of the following is correct about viroids?

Kepler's third law states that the square of the period of revolution (T) of a planet around the sun, is proportional to the third power of the average distance r between the sun and planet i.e. $T^2 = Kr^3$, here K is constant. If the masses of the sun and planet are M and m respectively, then as per Newton's law of gravitation, the force of attraction between them is $F = GMm/r^2$, here G is gravitational constant. The relation between G and K is described as:

A spherical ball is dropped into a long column of a highly viscous liquid. The graph that represents the speed of the ball ($v$) as a function of time ($t$) is: