JEE Main 2015 Physics Paper

An inductor $(L = 0.03\text{ H})$ and a resistor $(R = 0.15\text{ k}\Omega)$ are connected in series to a battery of $15\text{ V}\ \text{EMF}$ in a circuit shown below. The key $K_1$ has been kept closed for a long time. Then at $t = 0,\ K_1$ is opened and key $K_2$ is closed simultaneously. At $t = 1\text{ ms},$ the current in the circuit will be: $\left(e^5 \cong 150\right)$

An $LCR$ circuit is equivalent to a damped pendulum. In an $LCR$ circuit the capacitor is charged to $Q_0$ and then connected to the $L$ and $R$ as shown below:

If a student plots graphs of the square of maximum charge $\left(Q_{Max}^2\right)$ on the capacitor with time$(t)$ for two different values $L_1$ and $L_2\ (L_1 > L_2)$ of $L$ then which of the following represents this graph correctly?

(plots are schematic and not drawn to scale)

As an electron makes a transition from an excited state to the ground state of a hydrogen - like atom/ion:

In the given circuit, charges $Q_2$ on the $2\ \mu\text{F}$ capacitor changes as $C$ is varied from $1\ \mu\text{F}$ to $3\ \mu\text{F}.\ Q_2$ as a function of $'C'$ is given properly by:

$\text{(figures are drawn schematically and are not to scale)}$

Distance of the center of mass of a solid uniform cone from its vertex is $z_0$. If the radius of its base is $R$ and its height is $h$ then $z_0$ is equal to:

When $5\text{ V}$ potential difference is applied across a wire of length $0.1\text{ m},$ the drift speed of electrons is $2.5 \times 10^{-4}\text{ m s}^{-1}.$ If the electron density in the wire is $8 \times 10^{28}\text{ m}^{-3},$ the resistivity of the material is close to:

In the circuit shown, the current in the $1\ \Omega$ resistor is:

Match List - $\text{I}$ (Fundamental Experiment) with List - $\text{II}$ (its conclusion) and select the correct option

from the choices given below the list:

Two coaxial solenoids of different radius carry current $I$ in the same direction. $\vec{F_1}$ be the magnetic force on the inner solenoid due to the outer one and $\vec{F_2}$ be the magnetic force on the outer solenoid due to the inner one. Then:

A red $LED$ emits light at $0.1$ watt uniformly around it. The amplitude of the electric field of the light at a distance of $1\ m$ from the diode is:

A long cylindrical shell carries positive surface charge $\sigma$ in the upper half and negative surface charge - $\sigma$ in the lower half. The electric field lines around the cylinder will look like figure given in: (figures are schematic and not drawn to scale)

From a solid sphere of mass $M$ and radius $R,$ a spherical portion of radius $R/2$ is removed, as shown in the figure. Taking gravitational potential $V = 0$ at $r = \infty,$ the potential at the center of the cavity thus formed is:

($G = \text{gravitational constant}$)

Given in the figure are two blocks $A$ and $B$ of weight 20 N and 100 N, respectively. These are being pressed against a wall by a force $F$ as shown. If the coefficient of friction between the blocks is 0.1 and between block $B$ and the wall is 0.15, the frictional force applied by the wall on block $B$ is:

Two stones are thrown up simultaneously from the edge of a cliff $240\text{ m}$ high with initial speed of $10\text{ m/s}$ and $40\text{ m/s}$ respectively. Which of the following graph best represents the time variation of relative position of the second stone with respect to the first?

(Assume stones do not rebound after hitting the ground and neglect air resistance, take $g = 10\text{ m/s}^2$)

(The figures are schematic and not drawn to scale)

A rectangular loop of sides $10\text{ cm}$ and $5\text{ cm}$ carrying a current $I$ of $12\text{ A}$ is placed in different orientations as shown in the figures below:

If there is a uniform magnetic field of $0.3\text{ T}$ in the positive $z$ direction, in which orientations the loop would be in $(i)$ stable equilibrium and $(ii)$ unstable equilibrium?

Two long current carrying thin wires, both with current $I,$ are held by insulating threads of length $L$ and are in equilibrium as shown in the figure, with threads making an angle $\text{'}\theta\text{'}$ with the vertical. If wires have mass $\lambda$ per unit-length then the value of $I$ is:

($g =$ gravitational acceleration)

For a simple pendulum, a graph is plotted between its kinetic energy $(KE)$ and potential energy $(PE)$ against its displacement $d.$ Which one of the following represents these correctly? $\left(\textit{graphs are schematic and not drawn to scale}\right)$

A pendulum made of a uniform wire of cross sectional area $A$ has time period $T.$ When an additional mass $M$ is added to its bob, the time period changes to $T_M.$ If the Young's modulus of the material of the wire is $Y$ then $\frac{1}{Y}$ is equal to:

($g =$ gravitational acceleration)

The period of oscillation of a simple pendulum is $T = 2\pi\sqrt{\frac{L}{g}}$. Measured value of L is 20.0 cm known to 1 mm accuracy and time for 100 oscillations of the pendulum is found to be 90 s using wrist watch of 1 s resolution. The accuracy in the determination of g is:

Monochromatic light is incident on a glass prism of angle $A$. If the refractive index of the material of the prism is $\mu$, a ray, incident at an angle $\theta$. on the face $AB$ would get transmitted through the face $AC$ of the prism provided:

From a solid sphere of mass $M$ and radius $R$ a cube of maximum possible volume is cut. Moment of inertia of cube about an axis passing through its center and perpendicular to one of its face is:

A solid body of constant heat capacity $1\ J/{}^\circ C$ is being heated by keeping it in contact with reservoirs in two ways:

$(i)$ Sequentially keeping in contact with $2$ reservoirs such that each reservoir

supplies same amount of heat.

$(ii)$ Sequentially keeping in contact with $8$ reservoirs such that each reservoir

supplies same amount of heat.

In both the cases body is brought from initial temperature $100^\circ C$ to final temperature $200^\circ C$. Entropy change of the body in the two cases respectively is:

Consider a spherical shell of radius $R$ at temperature $T$. The black body radiation inside it can be considered as an ideal gas of photons with internal energy per unit volume $u = \frac{U}{V} \propto T^{4}$ and pressure $p = \frac{1}{3}\left(\frac{U}{V}\right)$. If the shell now undergoes an adiabatic expansion the relation between $T$ and $R$ is:

Consider an ideal gas confined in an isolated closed chamber. As the gas undergoes an adiabatic expansion, the average time of collision between molecules increases as $V^{q},$ where $V$ is the volume of the gas. The value of $q$ is: $\left(\gamma = \frac{C_p}{C_v}\right)$

A train is moving on a straight track with speed $20\text{ ms}^{-1}.$ It is blowing its whistle at the frequency of $1000\text{ Hz}$. The percentage change in the frequency heard by a person standing near the track as the train passes him is (speed of sound $= 320\text{ ms}^{-1}$) close to:

Assuming human pupil to have a radius of $0.25\text{ cm}$ and a comfortable viewing distance of $25\text{ cm}$, the minimum separation between two objects that human eye can resolve at $500\text{ nm}$ wavelength is:

On a hot summer night, the refractive index of air is smallest near the ground and increases with height from the ground. When a light beam is directed horizontally, the Huygens' principle leads us to conclude that as it travels, the light beam: