JEE Main 2023 Physics Paper: 29 Jan, Shift 1

A car is moving on a horizontal curved road with radius 50 m. The approximate maximum speed of car will be, if the coefficient of friction between tyres and road is 0.34. [take g = 10 ms $^{-2}$]

Ratio of thermal energy released in two resistors R and 3R connected in parallel in an electric circuit is:

In a metre bridge experiment the balance point is obtained if the gaps are closed by 2$\Omega$ and 3$\Omega$. A shunt of X $\Omega$ is added to 3$\Omega$ resistor to shift the balancing point by 22.5 cm. The value of X is ___________.

The threshold wavelength for photoelectric emission from a material is 5500 $\mathring{A}$. Photoelectrons will be emitted, when this material is illuminated with monochromatic radiation from a A. 75 W infra-red lamp

B. 10 W infra-red lamp

C. 75 W ultra-violet lamp

D. 10 W ultra-violet lamp

Choose the correct answer from the options given below:

A certain elastic conducting material is stretched into a circular loop. It is placed with its plane perpendicular to a uniform magnetic field B = 0.8 T. When released the radius of the loop starts shrinking at a constant rate of 2 cms $^{-1}$. The induced emf in the loop at an instant when the radius of the loop is 10 cm will be __________ mV.

Find the mutual inductance in the arrangement, when a small circular loop of wire of radius '$R$' is placed inside a large square loop of wire of side $L \ (L \gg R)$. The loops are coplanar and their centres coincide:

Which of the following are true?

A. Speed of light in vacuum is dependent on the direction of propagation.

B. Speed of light in a medium is independent of the wavelength of light.

C. The speed of light is independent of the motion of the source.

D. The speed of light in a medium is independent of intensity.

Choose the correct answer from the options given below:

A point charge $q_1 = 4q_0$ is placed at origin. Another point charge $q_2 = -q_0$ is placed at $x = 12$ cm. Charge of proton is $q_0$. The proton is placed on $x$ axis so that the electrostatic force on the proton is zero. In this situation, the position of the proton from the origin is ___________ cm.

In a cuboid of dimension $2L \times 2L \times L$, a charge $q$ is placed at the center of the surface '$S$' having area of $4L^{2}$. The flux through the opposite surface to '$S$' is given by

Two particles of equal mass '$m$' move in a circle of radius '$r$' under the action of their mutual gravitational attraction. The speed of each particle will be:

A block of mass $m$ slides down the plane inclined at angle $30^\circ$ with an acceleration $\frac{g}{4}$. The value of coefficient of kinetic friction will be:

A tennis ball is dropped on to the floor from a height of 9.8 m. It rebounds to a height 5.0 m. Ball comes in contact with the floor for 0.2s. The average acceleration during contact is ___________ ms $-2$.

(Given g = 10 ms $-2$)

A single current carrying loop of wire carrying current I flowing in anticlockwise direction seen from +ve $z$ direction and lying in $xy$ plane is shown in figure. The plot of $\hat{j}$ component of magnetic field (By) at a distance '$a$' (less than radius of the coil) and on $yz$ plane vs $z$ coordinate looks like

The magnitude of magnetic induction at mid point $\text{O}$ due to current arrangement as shown in Fig will be

If a radioactive element having half-life of $30\text{ min}$ is undergoing beta decay, the fraction of radioactive element remains undecayed after $90\text{ min}$. will be

A radioactive element ${}^{242}_{92}$X emits two $\alpha$-particles, one electron and two positrons. The product nucleus is represented by ${}^{234}_{\text{P}}$Y. The value of P is __________.

A solid sphere of mass 2 kg is making pure rolling on a horizontal surface with kinetic energy 2240 J. The velocity of centre of mass of the sphere will be _______ ms$^{-1}$.

Which one of the following statement is not correct in the case of light emitting diodes? A. It is a heavily doped p-n junction.

B. It emits light only when it is forward biased.

C. It emits light only when it is reverse biased.

D. The energy of the light emitted is equal to or slightly less than the energy gap of the semiconductor used.

Choose the correct answer from the options given below:

Surface tension of a soap bubble is $2.0 \times 10^{-2}\text{ N m}^{-1}$. Work done to increase the radius of soap bubble from $3.5\text{ cm}$ to $7\text{ cm}$ will be:

Take $\left[\pi = \frac{22}{7}\right]$

A bicycle tyre is filled with air having pressure of $270\text{ kPa}$ at $27^\circ\text{C}$. The approximate pressure of the air in the tyre when the temperature increases to $36^\circ\text{C}$ is

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

Assertion A: If $dQ$ and $dW$ represent the heat supplied to the system and the work done on the system respectively. Then according to the first law of thermodynamics $dQ = dU - dW$. Reason R: First law of thermodynamics is based on law of conservation of energy. In the light of the above statements, choose the correct answer from the options given below:

Match List I with List II:

Choose the correct answer from the options given below:

A person observes two moving trains, 'A' reaching the station and 'B' leaving the station with equal speed of $30\text{ m/s}$. If both trains emit sounds with frequency $300\text{ Hz}$, (Speed of sound: $330\text{ m/s}$) approximate difference of frequencies heard by the person will be:

Two simple harmonic waves having equal amplitudes of 8 cm and equal frequency of 10 Hz are moving along the same direction. The resultant amplitude is also 8 cm. The phase difference between the individual waves is _________ degree.

As shown in the figure, three identical polaroids P$1$, P$2$ and P$3$ are placed one after another. The pass axis of P$2$ and P$3$ are inclined at angle of 60${}^\circ$ and 90${}^\circ$ with respect to axis of P$1$. The source S has an intensity of 256 $\frac{W}{m^2}$. The intensity of light at point O is ____________ $\frac{W}{m^2}$.

In a Young's double slit experiment, two slits are illuminated with a light of wavelength $800\text{ nm}$. The line joining $A_1 P$ is perpendicular to $A_1 A_2$ as shown in the figure. If the first minimum is detected at $P$, the value of slits separation 'a' will be:

The distance of screen from slits D = 5 cm

A stone is projected at angle $30^\circ$ to the horizontal. The ratio of kinetic energy of the stone at point of projection to its kinetic energy at the highest point of flight will be -

A 0.4 kg mass takes 8s to reach ground when dropped from a certain height 'P' above surface of earth. The loss of potential energy in the last second of fall is __________ J.

(Take g = 10 m/s${}^{2}$)