List of practice Questions

For a particular ideal gas, which of the following graphs represents the variation of mean squared velocity of the gas molecules with temperature?

A force of 49 N acts tangentially at the highest point of a sphere (solid) of mass 20 kg, kept on a rough horizontal plane. If the sphere rolls without slipping, then the acceleration of the center of the sphere is

Three infinitely long wires with linear charge density \( \lambda \) are placed along the x-axis, y-axis and z-axis respectively. Which of the following denotes an equipotential surface?

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).
 Assertion (A): The binding energy per nucleon is found to be practically independent of the atomic number \( A \), for nuclei with mass numbers between 30 and 170. 
Reason (R): Nuclear force is long range. 
In the light of the above statements, choose the correct answer from the options given below:

Three parallel plate capacitors $ C_1 $, $ C_2 $, and $ C_3 $ each of capacitance 5 µF are connected as shown in the figure. The effective capacitance between points A and B, when the space between the parallel plates of $ C_1 $ capacitor is filled with a dielectric medium having dielectric constant of 4, is:

Two monochromatic light beams have intensities in the ratio 1:9. An interference pattern is obtained by these beams. The ratio of the intensities of maximum to minimum is


Consider two blocks A and B of masses \( m_1 = 10 \) kg and \( m_2 = 5 \) kg that are placed on a frictionless table. The block A moves with a constant speed \( v = 3 \) m/s towards the block B kept at rest. A spring with spring constant \( k = 3000 \) N/m is attached with the block B as shown in the figure. After the collision, suppose that the blocks A and B, along with the spring in constant compression state, move together, then the compression in the spring is, (Neglect the mass of the spring)

A resistor of value 200Ω and capacitance 15μF are connected in series. What is the total time constant of the circuit?
In an AC circuit, the EMF is 6 V. What will be the value of the current?

Given below are two statements: 
Statement (I) : The dimensions of Planck’s constant and angular momentum are same. 
Statement (II) : In Bohr’s model, electron revolves around the nucleus in those orbits for which angular momentum is an integral multiple of Planck’s constant. 
In the light of the above statements, choose the most appropriate answer from the options given below:

The displacement $ x $ versus time graph is shown below.
 
The displacement $ x $ is plotted against time $ t $. Choose the correct answer from the options given below:

The energy of a photon in a hydrogen atom is \( -13.6 \, \text{eV} \). What are the possible energies of the electron in other levels of the hydrogen atom?
The figure shows the arrangement of a magnetic dipole. What is the behavior of the magnetic field?
A 12W resistor is connected to a battery of 24V. What is the current through the resistor?
A wire of resistance R is bent into an equilateral triangle and an identical wire is bent into a square. The ratio of resistance between the two end points of an edge of the triangle to that of the square is:
A solid sphere is rolling without slipping on a horizontal plane. The ratio of the linear kinetic energy of the centre of mass of the sphere and rotational kinetic energy is:
A lens of focal length 20 cm in air is made of glass with a refractive index of 1.6. What is its focal length when it is immersed in a liquid of refractive index 1.8?
A fractional errors in $x$, $y$, and $z$ are $0.1$, $0.2$, and $0.5$ respectively. Find the maximum fractional error in $x^{-2} y^3 z^{-2}$.
A block of mass 2 kg is attached to one end of a massless spring whose other end is fixed at a wall. The spring-mass system moves on a frictionless horizontal table. The spring's natural length is 2 m and spring constant is 200 N/m. The block is pushed such that the length of the spring becomes 1 m and then released. At distance $ x $ m ($ x \leq 2 $) from the wall, the speed of the block will be:
A monochromatic light of frequency \( 5 \times 10^{14} \) Hz travelling through air, is incident on a medium of refractive index '2'. Wavelength of the refracted light will be :

A body of mass 1kg is suspended with the help of two strings making angles as shown in the figure. Magnitude of tensions $ T_1 $ and $ T_2 $, respectively, are (in N): 

In an LCR circuit, the current is calculated to be 141.4% of the initial value. What is the resonance condition for this circuit?
Two parallel wires carry currents of 5 A and 4 A in opposite directions. The wires are separated by a distance of 4 cm. Find the net magnetic field at a point midway between the two wires.
The fractional compression \( \frac{\Delta V}{V} \) of water at the depth of 2.5 km below the sea level is:
What is the lateral shift of a ray refracted through a parallel-sided glass slab of thickness \( h \) in terms of the angle of incidence \( i \) and angle of refraction \( r \), if the glass slab is placed in air medium?