JEE Main 2024 Solutions
JEE Main Physics (2024)

A particle is moving in one dimension (along $x$ axis) under the action of a variable force. Its initial position was 16 m right of origin. The variation of its position ($x$) with time ($t$) is given as $x = -3t^3 + 18t^2 + 16t$, where $x$ is in m and $t$ is in s. The velocity of the particle when its acceleration becomes zero is ________ m/s.

The displacement and the increase in the velocity of a moving particle in the time interval of $t$ to $(t + 1)$ seconds are 125 m and 50 m/s, respectively. The distance travelled by the particle in $(t + 2)^{\text{th}}$ second is ________ m.

The pressure and volume of an ideal gas related as $PV^{\frac{3}{2}} = K$ (Constant). The work done when the gas is taken from state A ($P_1, V_1, T_1$) to state B ($P_2, V_2, T_2$) is :

Two thermodynamical processes are shown in the figure. The molar heat capacity for process A and B are $C_A$ and $C_B$. The molar heat capacity at constant pressure and constant volume are represented by $C_P$ and $C_V$, respectively. Choose the correct statement.\n\n

$0.08\text{ kg}$ air is heated at constant volume through $5^\circ\text{C}$. The specific heat of air at constant volume is $0.17\text{ kcal/kg}^\circ\text{C}$ and $J = 4.18\text{ joule/cal}$. The change in its internal energy is approximately.

An object moves with speed $v_1, v_2$ and $v_3$ along a line segment AB, BC and CD respectively. If AB = BC and AD = 3AB, then the average speed of the object will be:

The radius ($r$), length ($l$) and resistance ($R$) of a metal wire was measured in the laboratory as\n$r = (0.35 \pm 0.05)\ \text{cm}$\n$R = (100 \pm 10)\ \Omega$\n$l = (15 \pm 0.2)\ \text{cm}$\nThe percentage error in the resistivity of the material of the wire is:

The dimensional formula of angular impulse is:

Match List-I with List-II:\n\n| List-I | List-II |\n|---|---|\n| (A) Coefficient of viscosity | (I) $[ML^2T^{-2}]$ |\n| (B) Surface tension | (II) $[ML^2T^{-1}]$ |\n| (C) Angular momentum | (III) $[ML^{-1}T^{-1}]$ |\n| (D) Rotational kinetic energy | (IV) $[ML^0T^{-2}]$ |\n\nChoose the correct answer from the options given below:

Given below are two statements:\n\nStatement (I): Planck's constant and angular momentum have same dimensions.\n\nStatement (II): Linear momentum and moment of force have same dimensions.\n\nIn the light of the above statements, choose the correct answer from the options given below:

A particle moving in a circle of radius $R$ with uniform speed takes time $T$ to complete one revolution. If this particle is projected with the same speed at an angle $\theta$ to the horizontal, the maximum height attained by it is equal to $4R$. The angle of projection $\theta$ is then given by:

Position of an ant (S in metres) moving in Y-Z plane is given by $S = 2t^2\hat{j} + 5\hat{k}$ (where $t$ is in second). The magnitude and direction of velocity of the ant at $t = 1$ s will be:

A particle starts from origin at $t = 0$ with a velocity $5\hat{i}$ m/s and moves in x-y plane under action of a force which produces a constant acceleration of $(3\hat{i} + 2\hat{j})\ \text{m/s}^2$. If the x-coordinate of the particle at that instant is 84 m, then the speed of the particle at this time is $\sqrt{\alpha}$ m/s. The value of $\alpha$ is ______.

A simple pendulum of length 1 m has a wooden bob of mass 1 kg. It is struck by a bullet of mass $10^{-2}$ kg moving with a speed of $2 \times 10^2\ \text{ms}^{-1}$. The bullet gets embedded into the bob. The height to which the bob rises before swinging back is: (use $g = 10\ \text{m/s}^2$)

A particle is placed at the point A of a frictionless track ABC as shown in figure. It is gently pushed towards right. The speed of the particle when it reaches the point B is: (Take $g = 10\ \text{m/s}^2$)\n\n

Two bodies of mass 4 g and 25 g are moving with equal kinetic energies. The ratio of magnitude of their linear momentum is:

Two moles of a monoatomic gas is mixed with six moles of a diatomic gas. The molar specific heat of the mixture at constant volume is:

At which temperature is the r.m.s. velocity of a hydrogen molecule equal to that of an oxygen molecule at 47°C?

The average kinetic energy of a monatomic molecule is 0.414 eV at temperature: (Use $K_B = 1.38 \times 10^{-23}\ \text{J/mol-K}$)

A tuning fork resonated with a sonometer wire of length 1 m stretched with a tension of 6 N. When the tension in the wire is changed to 54 N, the same tuning fork produces 12 beats per second with it. The frequency of the tuning fork is ______ Hz.

In a closed organ pipe, the frequency of fundamental note is 30 Hz. A certain amount of water is now poured in the organ pipe so that the fundamental frequency is increased to 110 Hz. If the organ pipe has a cross-sectional area of $2\ \text{cm}^2$, the amount of water poured in the organ tube is ______ g. (Take speed of sound in air is 330 m/s)

With rise in temperature, the Young's modulus of elasticity:

Young's modulus of material of a wire of length $L$ and cross-sectional area $A$ is $Y$. If the length of the wire is doubled and cross-sectional area is halved, then Young's modulus will be:

Each of three blocks P, Q and R shown in the figure has a mass of 3 kg. Each of the wires A and B has cross-sectional area $0.005\ \text{cm}^2$ and Young's modulus $2 \times 10^{11}\ \text{Nm}^{-2}$. Neglecting friction, the longitudinal strain on wire B is ______ $\times 10^{-4}$. (Take $g = 10\ \text{m/s}^2$)\n\n

If average depth of an ocean is 4000 m and the bulk modulus of water is $2 \times 10^9\ \text{Nm}^{-2}$, then fractional compression $\dfrac{\Delta V}{V}$ of water at the bottom of the ocean is $\alpha \times 10^{-2}$. The value of $\alpha$ is ______ . (Given, $g = 10\ \text{ms}^{-2}$, $\rho = 1000\ \text{kg m}^{-3}$)

The reading in the ideal voltmeter (V) shown in the given circuit diagram is:\n\n

The current in a conductor is expressed as $I = 3t^2 + 4t^3$, where $I$ is in Ampere and $t$ is in second. The amount of electric charge that flows through a section of the conductor during $t = 1\ \text{s}$ to $t = 2\ \text{s}$ is ______ C.

A potential divider circuit is shown in figure. The output voltage $V_0$ is:\n\n

An electric toaster has resistance of $60\ \Omega$ at room temperature ($27°C$). The toaster is connected to a 220 V supply. If the current flowing through it reaches 2.75 A, the temperature attained by toaster is around: (if $\alpha = 2 \times 10^{-4}/°C$)

Two cells are connected in opposition as shown. Cell $E_1$ is of 8 V emf and $2\ \Omega$ internal resistance; cell $E_2$ is of 2 V emf and $4\ \Omega$ internal resistance. The terminal potential difference of cell $E_2$ is ______ V.\n\n

A wire of length 10 cm and radius $\sqrt{7} \times 10^{-4}\ \text{m}$ is connected across the right gap of a meter bridge. When a resistance of $4.5\ \Omega$ is connected on the left gap by using a resistance box, the balance length is found to be at 60 cm from the left end. If the resistivity of the wire is $R \times 10^{-7}\ \Omega\text{m}$, then the value of $R$ is:

A wire of resistance $R$ and length $L$ is cut into 5 equal parts. If these parts are joined parallelly, then resultant resistance will be:

The charge accumulated on the capacitor connected in the following circuit is ______ $\mu$C. (Given $C = 150\ \mu\text{F}$)\n\n