List of practice Questions

Which of the following resistivity (\(\rho\)) vs temperature (T) curves is most suitable to be used in wire-bound standard resistors?

Sliding contact of a potentiometer is in the middle of the potentiometer wire having resistance \( R_p = 1 \, \Omega \) as shown in the figure. An external resistance of \( R_e = 2 \, \Omega \) is connected via the sliding contact.
The current \( i \) is :

Given below are two statements: Statement I : In a vernier callipers, one vernier scale division is always smaller than one main scale division. Statement II : The vernier constant is given by one main scale division multiplied by the number of vernier scale divisions. In light of the above statements, choose the correct answer from the options given below.

Given below are two statements: Statement-I: The equivalent emf of two nonideal batteries connected in parallel is smaller than either of the two emfs. Statement-II: The equivalent internal resistance of two nonideal batteries connected in parallel is smaller than the internal resistance of either of the two batteries. In light of the above statements, choose the correct answer from the options given below.

An electron is made to enters symmetrically between two parallel and equally but oppositely charged metal plates, each of 10 cm length. The electron emerges out of the field region with a horizontal component of velocity \(10^6\) m/s. If the magnitude of the electric field between the plates is 9.1 V/cm, then the vertical component of velocity of electron is (mass of electron = \(9.1 \times 10^{-31}\) kg and charge of electron = \(1.6 \times 10^{-19}\) C):

The work functions of cesium (Cs) and lithium (Li) metals are 1.9 eV and 2.5 eV, respectively. If we incident a light of wavelength 550 nm on these two metal surfaces, then photo-electric effect is possible for the case of:

A bob of mass \(m\) is suspended at a point \(O\) by a light string of length \(l\) and left to perform vertical motion (circular) as shown in the figure. Initially, by applying horizontal velocity \(v_0\) at the point ‘A’, the string becomes slack when the bob reaches at the point ‘D’. The ratio of the kinetic energy of the bob at the points B and C is:

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : If Young’s double slit experiment is performed in an optically denser medium than air, then the consecutive fringes come closer. Reason (R) : The speed of light reduces in an optically denser medium than air while its frequency does not change. In the light of the above statements, choose the most appropriate answer from the options given below :

A closed organ and an open organ tube filled by two different gases having the same bulk modulus but different densities \( \rho_1 \) and \( \rho_2 \), respectively. The frequency of the 9th harmonic of the closed tube is identical with the 4th harmonic of the open tube. If the length of the closed tube is 10 cm and the density ratio of the gases is \( \rho_1 : \rho_2 = 1 : 16 \), then the length of the open tube is:

Two spherical bodies of same materials having radii 0.2 m and 0.8 m are placed in same atmosphere. The temperature of the smaller body is 800 K and temperature of bigger body is 400 K. If the energy radiate from the smaller body is E, the energy radiated from the bigger body is (assume, effect of the surrounding to be negligible):

An electron in the ground state of the hydrogen atom has the orbital radius of \( 5.3 \times 10^{-11} \, \text{m} \) while that for the electron in the third excited state is \( 8.48 \times 10^{-10} \, \text{m} \). The ratio of the de Broglie wavelengths of the electron in the ground state to that in the excited state is:

An amount of ice of mass \( 10^{-3} \) kg and temperature \( -10^\circ C \) is transformed to vapor of temperature \( 110^\circ C \) by applying heat. The total amount of work required for this conversion is,
(Take, specific heat of ice = 2100 J kg\(^{-1}\) K\(^{-1}\),
specific heat of water = 4180 J kg\(^{-1}\) K\(^{-1}\),
specific heat of steam = 1920 J kg\(^{-1}\) K\(^{-1}\),
Latent heat of ice = \( 3.35 \times 10^5 \) J kg\(^{-1}\),
Latent heat of steam = \( 2.25 \times 10^6 \) J kg\(^{-1}\))

A proton is moving undeflected in a region of crossed electric and magnetic fields at a constant speed of \( 2 \times 10^5 \, \text{m/s} \). When the electric field is switched off, the proton moves along a circular path of radius 2 cm. The magnitude of electric field is \( x \times 10^4 \, \text{N/C} \). The value of \( x \) is \(\_\_\_\_\_\). (Take the mass of the proton as \( 1.6 \times 10^{-27} \, \text{kg} \)).

A tube of length L is shown in the figure. The radius of cross section at point (1) is 2 cm and at the point (2) is 1 cm, respectively. If the velocity of water entering at point (1) is 2 m/s, then velocity of water leaving the point (2) will be:

A conducting bar moves on two conducting rails as shown in the figure. A constant magnetic field \( B \) exists into the page. The bar starts to move from the vertex at time \( t = 0 \) with a constant velocity. If the induced EMF is \( E \propto t^n \), then the value of \( n \) is _____.

An electron projected perpendicular to a uniform magnetic field \( B \) moves in a circle. If Bohr’s quantization is applicable, then the radius of the electronic orbit in the first excited state is:

A ball of mass 100 g is projected with velocity 20 m/s at \( 60^\circ \) with horizontal. The decrease in kinetic energy of the ball during the motion from point of projection to highest point is:

Given below are two statements, one labeled as Assertion (A) and the other as Reason (R).
Assertion (A): In Young’s double slit experiment, the fringes produced by red light are closer compared to those produced by blue light.
Reason (R): The fringe width is directly proportional to the wavelength of light.
In the light of the above statements, choose the correct answer from the options given below:

A small rigid spherical ball of mass \( M \) is dropped in a long vertical tube containing glycerine. The velocity of the ball becomes constant after some time. If the density of glycerine is half of the density of the ball, then the viscous force acting on the ball will be (consider \( g \) as acceleration due to gravity):

Two long parallel wires X and Y, separated by a distance of 6 cm, carry currents of 5 A and 4 A, respectively, in opposite directions as shown in the figure. Magnitude of the resultant magnetic field at point P at a distance of 4 cm from wire Y is \( 3 \times 10^{-5} \) T. The value of \( x \), which represents the distance of point P from wire X, is\( \_\_\_\_\_\) cm. (Take permeability of free space as \( \mu_0 = 4\pi \times 10^{-7} \) SI units.)

To obtain the given truth table, the following logic gate should be placed at G

The volume contraction of a solid copper cube of edge length 10 cm, when subjected to a hydraulic pressure of \( 7 \times 10^6 \) Pa, would be _____ mm\(^3\). (Given bulk modulus of copper = \( 1.4 \times 10^{11} \) N m\(^{-2}\))

The torque due to the force \( \left( 2\hat{i} + \hat{j} + 2\hat{k} \right) \) about the origin, acting on a particle whose position vector is \( \hat{i} + \hat{j} + \hat{k} \), would be:

The maximum percentage error in the measurement of the density of a wire is: \[ \text{Given, mass of wire} = (0.60 \pm 0.003) \, \text{g}, \quad \text{radius of wire} = (0.50 \pm 0.01) \, \text{cm}, \quad \text{length of wire} = (10.00 \pm 0.05) \, \text{cm}. \]

The value of current \( I \) in the electrical circuit as given below, when the potential at \( A \) is equal to the potential at \( B \), will be _____ A.