List of practice Questions

Consider two satellites $S_1$ and $S_2$ with periods of revolution 1 hr. and 8 hr. respectively revolving around a planet in circular orbits. The ratio of angular velocity of satellite $S_1$ to the angular velocity of satellite $S_2$ is :

A particle of mass $m$ moves in a circular orbit under the central potential field, $U(r) = -\frac{C}{r}$, where $C$ is a positive constant. The correct radius – velocity graph of the particle's motion is:

If the angular velocity of earth's spin is increased such that the bodies at the equator start floating, the duration of the day would be approximately: [Take $g = 10$ ms⁻², $R = 6400 \times 10^3$ m, $\pi = 3.14$]

The angular momentum of a planet of mass $M$ moving around the sun in an elliptical orbit is $\vec{L}$. The magnitude of the areal velocity of the planet is:

The planet Mars has two moons, if one of them has a period 7 hours, 30 minutes and an orbital radius of $9.0 \times 10^3$ km. Find the mass of Mars.
$\left\{ \text{Given } \frac{4\pi^2}{G} = 6 \times 10^{11} \text{ N}^{-1} \text{ m}^{-2} \text{ kg}^2 \right\}$

Two identical particles of mass 1 kg each go round a circle of radius R under the action of their mutual gravitational attraction. The angular speed of each particle is :

The minimum and maximum distances of a planet revolving around the Sun are $x_1$ and $x_2$. If the minimum speed of the planet on its trajectory is $v_0$ then its maximum speed will be :

The time period of a satellite in a circular orbit of radius R is T. The period of another satellite in a circular orbit of radius 9R is :

A body weighs 49 N on a spring balance at the north pole. What will be its weight recorded on the same weighing machine, if it is shifted to the equator? [Use $g = \frac{GM}{R^2} = 9.8 \text{ ms}^{-2}$ and radius of earth, $R = 6400 \text{ km}$.]

A solid metal sphere of radius R having charge q is enclosed inside the concentric spherical shell of inner radius a and outer radius b as shown in figure. The approximate variation electric field $\vec{E}$ as a function of distance r from centre O is given by :

A uniformly charged disc of radius R having surface charge density $\sigma$ is placed in the xy plane with its center at the origin. Find the electric field intensity along the z-axis at a distance Z from origin :

Three capacitors C$_1$ = 2 $\mu$F, C$_2$ = 6 $\mu$F and C$_3$ = 12 $\mu$F are connected as shown in figure. Find the ratio of the charges on capacitors C$_1$, C$_2$ and C$_3$ respectively:

Figure shows a rod AB, which is bent in a 120$^{\circ}$ circular arc of radius R. A charge ($-Q$) is uniformly distributed over rod AB. What is the electric field $\vec{E}$ at the centre of curvature O?

Two particles A and B having charges $20\,\mu C$ and $-5\,\mu C$ respectively are held fixed with a separation of $5\,\text{cm}$. At what position a third charged particle should be placed so that it does not experience a net electric force ?

Choose the incorrect statement :
(a) The electric lines of force entering into a Gaussian surface provide negative flux.
(b) A charge 'q' is placed at the centre of a cube. The flux through all the faces will be the same.
(c) In a uniform electric field net flux through a closed Gaussian surface containing no net charge, is zero.
(d) When electric field is parallel to a Gaussian surface, it provides a finite non-zero flux.
Choose the most appropriate answer from the options given below :

A parallel plate capacitor of capacitance 200 $\mu F$ is connected to a battery of 200 V. A dielectric slab of dielectric constant 2 is now inserted into the space between plates of capacitor while the battery remains connected. The change in the electrostatic energy in the capacitor will be ________ J.

A charge 'q' is placed at one corner of a cube as shown in figure. The flux of electrostatic field $\vec{E}$ through the shaded area is:

Two small spheres each of mass 10 mg are suspended from a point by threads 0.5 m long. They are equally charged and repel each other to a distance of 0.20 m. The charge on each of the sphere is $\frac{a}{21} \times 10^{-8}$ C. The value of 'a' will be ________ . [Given g=10 ms⁻²]

Two identical conducting spheres with negligible volume have 2.1 nC and –0.1 nC charges, respectively. They are brought into contact and then separated by a distance of 0.5 m. The electrostatic force acting between the spheres is ________ $\times$ 10⁻⁹ N. [Given : $4\pi\epsilon_0 = \frac{1}{9 \times 10^9}$ SI unit]

Two capacitors of capacities 2C and C are joined in parallel and charged up to potential V. The battery is removed and the capacitor of capacity C is filled completely with a medium of dielectric constant K. The potential difference across the capacitors will now be :

In the reported figure, a capacitor is formed by placing a compound dielectric between the plates of parallel plate capacitor. The expression for the capacity of the said capacitor will be : (Given area of plate = A)

Two identical tennis balls each having mass 'm' and charge 'q' are suspended from a fixed point by threads of length 'l'. What is the equilibrium separation when each thread makes a small angle '$\theta$' with the vertical ?

512 identical drops of mercury are charged to a potential of 2 V each. The drops are joined to form a single drop. The potential of this drop is ______ V.

The electric field is $\vec{E} = \left( \frac{3}{5} E_0 \hat{i} + \frac{4}{5} E_0 \hat{j} \right)$. The ratio of flux through surface of area 0.2 m² (parallel to y-z plane) to that of area 0.3 m² (parallel to x-z plane) is a : b, where a = _________.

Two equal capacitors are first connected in series and then in parallel. The ratio of the equivalent capacities in the two cases will be :