JEE Main 2023 Physics Question Paper Jan 30 Shift 2- Download Paper with Solution PDF Here

Physics
Section-A

Question 1:

A block of \( \sqrt{3} \, kg \) is attached to a string whose other end is attached to the wall. An unknown force \( F \) is applied so that the string makes an angle of \( 30^\circ \) with the wall. The tension \( T \) is:

(Given \( g = 10 \, ms^{-2} \))

A flask contains hydrogen and oxygen in the ratio of 2 : 1 by mass at temperature 27°C. The ratio of average kinetic energy per molecule of hydrogen and oxygen respectively is:

The equivalent resistance between A and B is ......

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.

Assertion A: The nuclear density of nuclides \( ^{10}_5 B, \, ^{6}_3 Li, \, ^{56}_{26} Fe, \, ^{20}_10 Ne \) and \( ^{209}_{83} Bi \) can be arranged as \[ N_{Bi} > N_{Fe} > N_{Ne} > N_{Pb}. \]

Reason R: The radius \( R \) of the nucleus is related to its mass number \( A \) as \( R = R_0 A^{1/3} \), where \( R_0 \) is a constant.

In the light of the above statement, choose the correct answer from the options given below:

• (1) Both A and R are true and R is the correct explanation of A
• (2) A is false but R is true
• (3) A is true but R is false
• (4) Both A and R are true but R is NOT the correct explanation of A

A thin prism \( P_1 \) with an angle of \( 6^\circ \) and made of glass of refractive index 1.54 is combined with another prism \( P_2 \) made from glass of refractive index 1.72 to produce dispersion without average deviation. The angle of prism \( P_2 \) is:

• (1) \( 6^\circ \)
• (2) \( 1.3^\circ \)
• (3) \( 7.8^\circ \)
• (4) \( 4.5^\circ \)

The output Y for the inputs A and B of the circuit is given by:

A vehicle travels 4 km with a speed of 3 km/h and another 4 km with a speed of 5 km/h, then its average speed is:

• (1) 4.25 km/h
• (2) 3.50 km/h
• (3) 4.00 km/h
• (4) 3.75 km/h

As shown in the figure, a point charge Q is placed at the centre of a conducting spherical shell of inner radius a and outer radius b. The electric field due to charge Q in three different regions I, II, and III is given by: (I : r < a, II : a < r < b, III : r > b)

• (1) \( E_I = 0, E_{II} = 0, E_{III} \neq 0 \)
• (2) \( E_I \neq 0, E_{II} = 0, E_{III} = 0 \)
• (3) \( E_I = 0, E_{II} = 0, E_{III} = 0 \)
• (4) \( E_I = 0, E_{II} \neq 0, E_{III} = 0 \)

As shown in the figure, a current of 2A flowing in an equilateral triangle of side \(4\sqrt{3}\) cm. The magnetic field at the centroid O of the triangle is:

• (1) \(4\sqrt{3} \times 10^{-4} \, T\)
• (2) \(4\sqrt{3} \times 10^{-5} \, T\)
• (3) \(\sqrt{3} \times 10^{-4} \, T\)
• (4) \(3\sqrt{3} \times 10^{-5} \, T\)

In the given circuit, rms value of current (\(I_{rms}\)) through the resistor \(R\) is:

• (1) \(2A\)
• (2) \(\frac{1}{2}A\)
• (3) \(20A\)
• (4) \(2\sqrt{2}A\)

A machine gun of mass 10 kg fires 20 g bullets at the rate of 180 bullets per minute with a speed of 100 m/s each. The recoil velocity of the gun is:

• (1) 0.02 m/s
• (2) 2.5 m/s
• (3) 1.5 m/s
• (4) 0.6 m/s

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: Efficiency of a reversible heat engine will be highest at –273°C temperature of cold reservoir.

Reason R: The efficiency of Carnot’s engine depends not only on the temperature of cold reservoir but it depends on the temperature of hot reservoir too and is given as: \[ \eta = \left( 1 - \frac{T_2}{T_1} \right) \]

In the light of the above statements, choose the correct answer from the options given below:

• (1) A is true but R is false
• (2) Both A and R are true but R is NOT the correct explanation of A
• (3) A is false but R is true
• (4) Both A and R are true and R is the correct explanation of A

Match List I with List II.




Choose the correct answer from the options given below:

• (1) A-IV, B-III, C-I, D-II
• (2) A-I, B-IV, C-III, D-II
• (3) A-IV, B-I, C-II, D-III
• (4) A-IV, B-I, C-III, D-II

For a simple harmonic motion in a mass spring system shown, the surface is frictionless. When the mass of the block is 1 kg, the angular frequency is \(\omega_1\). When the mass block is 2 kg the angular frequency is \(\omega_2\). The ratio \(\frac{\omega_2}{\omega_1}\) is:

• (1) \(\sqrt{2}\)
• (2) \(\frac{1}{\sqrt{2}}\)
• (3) 2
• (4) \(\frac{1}{2}\)

An electron accelerated through a potential difference \(V_1\) has a de-Broglie wavelength of \(\lambda\). When the potential is changed to \(V_2\), its de-Broglie wavelength increases by 50%. The value of \( \frac{V_1}{V_2} \) is equal to :

• (1) 3
• (2) \( \frac{9}{4} \)
• (3) \( \frac{3}{2} \)
• (4) 4

Match List I with List II:





Choose the correct answer from the options given below:

• (1) A-I, B-II, C-III, D-IV
• (2) A-II, B-III, C-IV, D-I
• (3) A-IV, B-III, C-I, D-II
• (4) A-IV, B-III, C-II, D-I

A current carrying rectangular loop PQRS is made of uniform wire. The length PR = QS = 5 cm and PQ = RS = 100 cm. If ammeter current reading changes from I to 2I, the ratio of magnetic forces per unit length on the wire PQ due to wire RS in the two cases respectively is :

• (1) 1 : 2
• (2) 1 : 4
• (3) 1 : 5
• (4) 1 : 3

A force is applied to a steel wire ‘A’, rigidly clamped at one end. As a result, elongation in the wire is 0.2 mm. If same force is applied to another steel wire ‘B’ of double the length and a diameter 2.4 times that of the wire ‘A’, the elongation in the wire ‘B’ will be (wires having uniform circular cross sections):

• (1) \( 6.06 \times 10^{-2} \) mm
• (2) \( 2.77 \times 10^{-2} \) mm
• (3) \( 3.0 \times 10^{-2} \) mm
• (4) \( 6.9 \times 10^{-2} \) mm

An object is allowed to fall from a height \(R\) above the earth, where \(R\) is the radius of the earth. Its velocity when it strikes the earth’s surface, ignoring air resistance, will be:

• (1) \( 2\sqrt{gR} \)
• (2) \( \sqrt{gR} \)
• (3) \( \frac{\sqrt{gR}}{2} \)
• (4) \( \sqrt{2gR} \)

A point source of 100 W emits light with 5% efficiency. At a distance of 5 m from the source, the intensity produced by the electric field component is:

• (1) \( \frac{1}{2\pi} \, W/m^2 \)
• (2) \( \frac{1}{40\pi} \, W/m^2 \)
• (3) \( \frac{1}{10\pi} \, W/m^2 \)
• (4) \( \frac{1}{20\pi} \, W/m^2 \)

Section-B

Question 21:

A faulty thermometer reads 5°C in melting ice and 95°C in steam. The correct temperature on absolute scale will be ........ K when the faulty thermometer reads 41°C.

If the potential difference between B and D is zero, the value of \(x\) is \( \frac{1}{n} \Omega \). The value of \(n\) is ........

The velocity of a particle executing SHM varies with displacement (\(x\)) as \(4v^2 = 50 - x^2\). The time period of oscillations is \( \frac{x}{7} \). The value of \(x\) is ........

In a Young’s double slit experiment, the intensities at two points, for the path difference \( \frac{\lambda}{4} \) and \( \frac{\lambda}{3} \) (where \( \lambda \) is the wavelength of light used), are \( I_1 \) and \( I_2 \) respectively. If \( I_0 \) denotes the intensity produced by each of the individual slits, then \[ \frac{I_1 + I_2}{I_0} = \ldots \]

A radioactive nucleus decays by two different processes. The half-life of the first process is 5 minutes and that of the second process is 30s. The effective half-life of the nucleus is calculated to be \( \frac{\alpha}{11} \) seconds. The value of \( \alpha \) is ..............

A body of mass 2 kg is initially at rest. It starts moving unidirectionally under the influence of a source of constant power P. Its displacement in 4s is \( \frac{1}{3} \alpha^2 \sqrt{P} \) meters. The value of \( \alpha \) will be ...........

As shown in figure, a cuboid lies in a region with electric field \( \mathbf{E} = 2x^2 \hat{i} - 4y \hat{j} + 6 \hat{k} \) N/C. The magnitude of charge within the cuboid is \( n \epsilon_0 \) C. The value of \( n \) is ....... (if dimensions of cuboid are \( 1 \times 2 \times 3 \, m^3 \))

In an ac generator, a rectangular coil of 100 turns each having area \( 14 \times 10^{-2} \, m^2 \) is rotated at 360 rev/min about an axis perpendicular to a uniform magnetic field of magnitude 3.0 T. The maximum value of the emf produced will be .......... V. (Take \( \pi = \frac{22}{7} \))

A stone tied to 180 cm long string at its end is making 28 revolutions in a horizontal circle in every minute. The magnitude of acceleration of stone is \(\frac{1936}{x} \, m/s^2\). The value of \(x\) is .........

A uniform disc of mass 0.5 kg and radius \(r\) is projected with velocity 18 m/s at \(t = 0\) on a rough horizontal surface. It starts off with a purely sliding motion at \(t = 0\). After 2s, it acquires a purely rolling motion (see figure). The total kinetic energy of the disc after 2s will be ......... J (given, coefficient of friction is 0.3 and \(g = 10 \, m/s^2\)).