MHT CET 2023 Physics Paper: 11 May, Shift 2

The a.c. source of e.m.f. with instantaneous value '$e$' is given by $e = 200 \sin(50t)$ volt. The r.m.s. value of current in a circuit of resistance $50\ \Omega$ is

In a series LCR circuit, $C = 2\ \mu\text{F}, L = 1\text{ mH}$ and $R = 10\ \Omega$. The ratio of the energies stored in the inductor and the capacitor, when the maximum current flows in the circuit, is

The a.c. source is connected to series LCR circuit. If voltage across $R$ is $40\text{ V}$, that across $L$ is $80\text{ V}$ and that across $C$ is $40\text{ V}$, then the e.m.f. '$e$' of a.c. source is

The orbital magnetic moment associated with orbiting electron of charge '$e$' is

Bohr model is applied to a particle of mass '$m$' and charge '$q$' moving in a plane under the influence of a transverse magnetic field '$B$'. The energy of the charged particle in the $n$th leve will be $[h =$ Planck's constant $]$

According to Bohr's theory of hydrogen atom, the total energy of the electron in the $n$th stationary orbit is

Two spherical conductors of capacities $3\ \mu\text{F}$ and $2\ \mu\text{F}$ are charged to same potential having radii $3\text{ cm}$ and $2\text{ cm}$ respectively. If '$\sigma_1$ ' and '$\sigma_2$' represent surface density of charge on respective conductors then $\frac{\sigma_1}{\sigma_2}$ is

Three identical capacitors of capacitance '$C$' each are connected in series and this connection is connected in parallel with one more such identical capacitor. Then the capacitance of whole combination is

A parallel plate capacitor is charged by a battery and battery remains connected. The dielectric slab of constant '$K$' is inserted between the plates and then taken out. Then electric field between the plates

In a conical pendulum the bob of mass '$m$' moves in a horizontal circle of radius '$r$' with uniform speed '$V$'. The string of length '$L$' describes a cone of semi vertical angle '$\theta$'. The centripetal force acting on the bob is ( $g =$ acceleration due to gravity)

Two batteries, one of e.m.f. $12\text{ V}$ and internal resistance $2\ \Omega$ and other of e.m.f. $6\text{ V}$ and internal resistance $1\ \Omega$, are connected as shown in the figure. What will be the reading of the voltmeter 'V'?

Potential difference between the points P and Q is nearly

A metal surface of work function $1.13\text{ eV}$ is irradiated with light of wavelength $310\text{ nm}$. The retarding potential required to stop the escape of photoelectrons is [Take $\frac{hc}{e} = 1240 \times 10^{-9}\text{ SI}$ units]

When a metallic surface is illuminated with radiation of wavelength '$\lambda$', the stopping potential is '$V$'. If the same surface is illuminated with radiation of wavelength '$2\lambda$', the stopping potential is ' $\left(\frac{V}{4}\right)$ '. The threshold wavelength for the metallic surface is

A coil having effective area '$A$' is held with its plane normal to a magnitude field of induction '$B$'. The magnetic induction is quickly reduced to $25\%$ of its initial value in 1 second. The e.m.f. induced in the coil (in volt) will be

The magnetic flux through a circuit of resistance '$R$' changes by an amount $\Delta\phi$ in the time $\Delta t$. The total quantity of electric charge '$Q$' which passes during this time through any point of the circuit is

The self inductance '$L$' of a solenoid of length '$l$' and area of cross-section '$A$', with a fixed number of turns '$N$' increases as

An electromagnetic wave, whose wave normal makes an angle of $45^\circ$ with the vertical, travelling in air strikes a horizontal liquid surface. While travelling through the liquid it gets deviated through $15^\circ$. What is the speed of the electromagnetic wave in the liquid, if the speed of electromagnetic wave in air is $3 \times 10^{8}\text{ m/s}$? $\left(\sin 30^\circ = 0.5, \sin 45^\circ = \frac{1}{\sqrt{2}}\right)$

An electron of mass '$m$' and charge '$q$' is accelerated from rest in a uniform electric field of strength '$E$'. The velocity acquired by the electron, when it travels a distance '$L$', is

A fluid of density '$\rho$' is flowing through a uniform tube of diameter '$d$'. The coefficient of viscosity of the fluid is '$\eta$', then critical velocity of the fluid is

The ratio of energy required to raise a satellite to a height '$h$' above the earth's surface to that required to put it into the orbit at the same height is ($R =$ radius of earth)

The radius of the orbit of a geostationary satellite is (mean radius of earth is '$R$', angular velocity about own axis is '$\omega$' and acceleration due to gravity on earth's surface is '$g$')

Two bodies $A$ and $B$ at temperatures '$T_1$' $\text{K}$ and '$T_2$' $\text{K}$ respectively have the same dimensions. Their emissivities are in the ratio $1 : 3$. If they radiate the same amount of heat per unit area per unit time, then the ratio of their temperatures $(T_1 : T_2)$ is

If temperature of gas molecules is raised from $127^\circ\text{C}$ to $527^\circ\text{C}$, the ratio of r.m.s. speed of the molecules is respectively

Two cars A and B start from a point at the same time in a straight line and their positions are represented by $R_A(t) =$ at $+bt^2$ and $R_B(t) = xt - t^2$. At what time do the cars have same velocity?

A circular arc of radius '$r$' carrying current '$I$' subtends an angle $\frac{\pi}{16}$ at its centre. The radius of a metal wire is uniform. The magnetic induction at the centre of circular arc is $[\mu_0 =$ permeability of free space]

Two long conductors separated by a distance '$d$' carry currents $I_1$ and $I_2$ in the same direction. They exert a force '$F$' on each other. Now the current in one of them is increased to two times and its direction is reversed. The distance between them is also increased to $3d$. The new value of force between them is

The upper end of the spring is fixed and a mass '$m$' is attached to its lower end. When mass is slightly pulled down and released, it oscillates with time period 3 second. If mass '$m$' is increased by $1\text{ kg}$, the time period becomes 5 second. The value of '$m$' is (mass of spring is negligible)

A double convex lens of focal length '$F$' is cut into two equal parts along the vertical axis. The focal length of each part will be

From a disc of mass '$M$' and radius '$R$', a circular hole of diameter '$R$' is cut whose rim passes through the centre. The moment of inertia of the remaining part of the disc about perpendicular axis passing through the centre is

Two bodies have their moments of inertia I and 2I respectively about their axis of rotation. If their kinetic energies of rotation are equal, their angular momenta will be in the ratio

In the study of transistor as an amplifier if $\alpha = \frac{I_C}{I_E} = 0.98$ and $\beta = \frac{I_C}{I_B} = 49$, where $I_C, I_B$ and $\text{I}_\text{E}$ are collector, base and emitter current respectively then $\left(\frac{1}{\alpha} - \frac{1}{\beta}\right)$ is equal to

In the digital circuit the inputs are as shown in figure. The Boolean expression for output $\mathrm{Y}$ is

If $p\text{-}n$ junction diode is in forward bias then

What should be the diameter of a soap bubble, in order that the excess pressure inside it is $25.6\text{ N m}^{-2}$? [surface tension of soap $= 3.2 \times 10^{-2}\text{ N m}^{-1}]$

A liquid drop of radius '$R$' is broken into '$n$' identical small droplets. The work done is [T = surface tension of the liquid]

According to Boyle's law, the product PV remains constant. The unit of $PV$ is same as that of

For a gas, $\frac{R}{C_v} = 0.4$, where $R$ is universal gas constant and $C_v$ is molar specific heat at constant volume. The gas is made up of molecules which are

An ideal gas expands adiabatically. $(\gamma = 1.5)$ To reduce the r.m.s. velocity of the molecules 3 times, the gas has to be expanded

The difference in length between two rods $\text{A}$ and $\text{B}$ is $60\text{ cm}$ at all temperatures. If $\alpha_{\text{A}} = 18 \times 10^{-6}/^\circ\text{C}$ and $\alpha_{\text{B}} = 27 \times 10^{-6}/^\circ\text{C}$, the lengths of the two rods are

The path difference between two waves, represented by $y_1 = a_1\sin\left(\omega t - \frac{2\pi x}{\lambda}\right)$ and $y_2 = a_2\cos\left(\omega t - \frac{2\pi x}{\lambda} + \phi\right)$ is

A transverse wave in a medium is given by $y = A\sin 2(\omega t - kx)$. It is found that the magnitude of the maximum velocity of particles in the medium is equal to that of the wave velocity. What is the value of $A$?

Two progressive waves are travelling towards each other with velocity $50\text{ m/s}$ and frequency $200\text{ Hz}$. The distance between the two consecutive antinodes is

A sonometer wire '$A$' of diameter '$d$' under tension '$T$' having density '$\rho_1$' vibrates with fundamental frequency '$n$'. If we use another wire '$B$' which vibrates with same frequency under tension '$2T$' and diameter '$2d$' then density '$\rho_2$ ' of wire '$B$' will be

A sound of frequency $480\text{ Hz}$ is emitted from the stringed instrument. The velocity of sound in air is $320\text{ m/s}$. After completing 180 vibrations, the distance covered by a wave is

A rectangular block of mass '$m$' and crosssectional area A, floats on a liquid of density '$\rho$'. It is given a small vertical displacement from equilibrium, it starts oscillating with frequency '$n$' equal to ( $g =$ acceleration due to gravity)

A beam of light of wavelength $600\text{ nm}$ from a distant source falls on a single slit $1\text{ mm}$ wide and the resulting diffraction pattern is observed on a screen $2\text{ m}$ away. The distance between the first dark fringe on either side of the central bright fringe is

In Young's double slit experiment, green light is incident on two slits. The interference pattern is observed on a screen. Which one of the following changes would cause the observed fringes to be more closely spaced?

In Young's double slit experiment, the fifth maximum with wavelength '$\lambda_1$ ' is at a distance '$y_1$' and the same maximum with wavelength '$\lambda_2$' is at a distance '$y_2$ ' measured from the central bright band. Then $\frac{y_1}{y_2}$ is equal to [D and $d$ are constant]