Question Bank Directory

A body projected vertically from the earth reaches a height equal to earth’s radius before returning to the earth. The power exerted by the gravitational force:

An increase in the temperature of a gas-filled container would lead to:

A particle of mass $m$ is projected with a velocity, $v = kv_e$ ($k < 1$) from the surface of the earth. The maximum height, above the surface, reached by the particle is: (Where $v_e = $ escape velocity, $R = $ the radius of the earth)

An electric dipole is placed as shown in the figure. The electric potential (in 10² V) at the point P due to the dipole is: (ε₀ = permittivity of free space and 1/4πε₀ = k)

A satellite is orbiting just above the surface of the earth with period $T$. If $d$ is the density of the earth and $G$ is the universal constant of gravitation, the quantity $\frac{3\pi}{Gd}$ represents:

The molecular weight of two gases is $M_1$ and $M_2$. At any temperature, the ratio of root mean square velocities $v_1$ and $v_2$ will be:

Assuming the earth to be a sphere of uniform density, its acceleration due to gravity acting on a body:

Which one of the following plots represent the variation of gravitational field on a particle at distance $r$, due to a thin spherical shell of radius $R$? ($r$ is measured from the centre of the spherical shell).

Two charged spherical conductors of radii $R_1$ and $R_2$ are connected by a wire. The ratio of surface charge densities of spheres $(\sigma_1/\sigma_2)$ is:

Assuming that the gravitational potential energy of an object at infinity is zero, the change in potential energy (final - initial) of an object of mass $m$ when taken to a height $h$ from the surface of the earth (of radius $R$ and mass $M$), is given by:

The ratio of frequencies of fundamental harmonic produced by an open pipe to that of closed pipe having the same length is:

In a gravitational field, the gravitational potential is given by $V=-\frac{K}{x}$ J/kg. The gravitational field intensity at the point $(2,0,3)$ m is:

Two satellites of Earth, $S_1$ and $S_2$, are moving in the same orbit. The mass of $S_1$ is four times the mass of $S_2$. Which one of the following statements is true?

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:

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 $k_B = 1.38 \times 10^{-23} \text{ J K}^{-1}$)