MHT CET 2023 Physics Paper: 9 May, Shift 2

An alternating voltage of frequency '$\omega$' is induced in electric circuit consisting of an inductance '$L$' and capacitance '$C$', connected in parallel. Then across the inductance coil

The reactance of capacitor at $50\text{ Hz}$ is $5\ \Omega$. If the frequency is increased to $100\text{ Hz}$, the new reactance is

An e.m.f. $E = 4\cos(1000t)$ volt is applied to an LR circuit of inductance $3\text{ mH}$ and resistance $4\ \Omega$. The maximum current in the circuit is

The force acting on the electron in hydrogen atom (Bohr' theory) is related to the principle quantum number '$n$' as

The wavelength of light for the least energetic photons emitted in the Lyman series of the hydrogen spectrum is nearly [Take $hc = 1240\text{ eV}\cdot\text{nm}$, change in energy of the levels $= 10.2\text{ eV}$ ]

A parallel combination of two capacitors of capacities '$2C$' and '$C$' is connected across $5\text{ V}$ battery. When they are fully charged, the charges and energies stored in them be '$Q_1$ ', '$Q_2$' and '$E_1$ ', '$E_2$' respectively. Then $\frac{E_1-E_2}{Q_1-Q_2}$ in $\text{J/C}$ is (capacity is in Farad, charge in Coulomb and energy in J)

A particle at rest starts moving with constant angular acceleration $4\text{ rad/s}^2$ in circular path. At what time the magnitudes of its tangential acceleration and centrifugal acceleration will be equal?

A particle of mass '$m$' moves along a circle of radius '$r$' with constant tangential acceleration. If K.E. of the particle is '$E$' by the end of third revolution after beginning of the motion, then magnitude of tangential acceleration is

A simple pendulum of length $2\text{ m}$ is given a horizontal push through angular displacement of $60^\circ$. If the mass of bob is 200 gram, the angular velocity of the bob will be (Take Acceleration due to gravity $= 10\text{ m/s}^2$) $\left(\sin 30^\circ = \cos 60^\circ = 0.5, \cos 30^\circ = \sin 60^\circ = \sqrt{3}/2\right)$

Five current carrying conductors meet at a point '$\text{O}$' as shown in figure. The magnitude and direction of the current in conductor '$OP$' is

A galvanometer of resistance $20\ \Omega$ gives a deflection of 5 divisions when $1\text{ mA}$ current flows through it. The galvanometer scale has 50 divisions. To convert the galvanometer into a voltmeter of range 25 volt, we should connect a resistance of

When photons of energies twice and thrice the work function of a metal are incident on the metal surface one after other, the maximum velocities of the photoelectrons emitted in the two cases are $v_1$ and $v_2$ respectively. The ratio $v_1 : v_2$ is

When a certain metal surface is illuminated with light of frequency $\nu$, the stopping potential for photoelectric current is $V_0$. When the same surface is illuminated by light of frequency $\frac{\nu}{2}$, the stopping potential is $\frac{V_0}{4}$, the threshold frequency of photoelectric emission is

If current '$I$' is flowing in the closed circuit with collective resistance '$R$', the rate of production of heat energy in the loop as we pull it along with a constant speed '$V$' is ( $L =$ length of conductor, $B =$ magnetic field)

Two coils $A$ and $B$ have mutual inductance 0.008 $\text{H}$. The current changes in the coil A, according to the equation $I = I_m \sin \omega t$, where $I_m = 5\text{ A}$ and $\omega = 200\pi\text{ rad s}^{-1}$. The maximum value of the e.m.f. induced in the coil $B$ in volt is

The mutual inductance (M) of the two coils is $3\text{ H}$. The self inductances of the coils are $4\text{ H}$ and $9\text{ H}$ respectively. The coefficient of coupling between the coils is

A charge '$q$' moves with velocity '$v$' through electric (E) as well as magnetic field (B). Then the force acting on it is

When a charge of $3\text{ C}$ is placed in uniform electric field, it experiences a force of $3000\text{ N}$. Within this field, potential difference between two points separated by a distance of $1\text{ cm}$ is

The charges $2q, -q, -q$ are located at the vertices of an equilateral triangle. At the circumcentre of the triangle

A fluid of density '$\rho$' and viscosity '$\eta$' is flowing through a pipe of diameter '$d$', with a velocity '$v$'. Reynold number is

Consider a planet whose density is same as that of the earth but whose radius is three times the radius '$R$' of the earth. The acceleration due to gravity '$g_n$' on the surface of planet is $g_n = x$. $g$ where $g$ is acceleration due to gravity on surface of earth. The value of '$x$' is

Periodic time of a satellite revolving above the earth's surface at a height equal to radius of the earth '$R$' is [ $g =$ acceleration due to gravity]

The pressure exerted by an ideal gas at a particular temperature is directly proportional to

The temperature of an ideal gas is increased from $27^\circ\text{C}$ to $927^\circ\text{C}$. The r.m.s. speed of its molecules becomes

An ideal gas in a container of volume 500 c.c. is at a pressure of $2 \times 10^{+5}\text{ N/m}^{2}$. The average kinetic energy of each molecule is $6 \times 10^{-21}\text{ J}$. The number of gas molecules in the container is

A thin rod of length $L$ has magnetic moment $M$ when magnetised. If rod is bent in a semicircular arc what is magnetic moment in new shape?

10 A current is flowing in two straight parallel wires in the same direction. Force of attraction between them is $1 \times 10^{-3}\text{ N}$. If the current is doubled in both the wires the force will be

The magnetic field at a point $P$ situated at perpendicular distance '$R$' from a long straight wire carrying a current of $12\text{ A}$ is $3 \times 10^{-5}\text{ Wb/m}^2$. The value of '$R$' in $\text{mm}$ is $\left[\mu_0 = 4\pi \times 10^{-7}\text{ Wb/Am}\right]$

A particle is vibrating in S.H.M. with an amplitude of $4\text{ cm}$. At what displacement from the equilibrium position is its energy half potential and half kinetic?

Two S.H.Ms. are represented by equations $y_1 = 0.1\sin\left(100\pi t + \frac{\pi}{3}\right)$ and $y_2 = 0.1\cos(100\pi t)$ The phase difference between the speeds of the two particles is

A spring has a certain mass suspended from it and its period for vertical oscillations is '$T_1$'. The spring is now cut in to two equal halves and the same mass is suspended from one of the halves. The period of vertical oscillations is now '$T_2$ '. The ratio $T_1/T_2$ is

A transparent glass cube of length $24\text{ cm}$ has a small air bubble trapped inside. When seen normally through one surface from air outside, its apparent distance is $10\text{ cm}$ from the surface. When seen normally from opposite surface, its apparent distance is $6\text{ cm}$. The distance of the air bubble from first surface is

If a ray of light in denser medium strikes a rarer medium at angle of incidence $i$, the angles of reflection and refraction are $r$ and $r'$ respectively. If the reflected and refracted rays are at right angles to each other, the critical angle for the given pair of media is

A disc of radius $R$ and thickness $\frac{R}{6}$ has moment of inertia I about an axis passing through its centre and perpendicular to its plane. The disc is melted and recast into a solid sphere. The moment of inertia of a sphere about its diameter is

In a transistor, in common emitter configuration, the ratio of power gain to voltage gain is

In the reverse biasing of a p-n junction diode:

If the frequency of the input voltage is $50\text{ Hz}$, applied to a (a) half wave rectifier and (b) full wave rectifier. The output frequency in both cases is respectively

A soap bubble of radius '$R$' is blown. After heating a solution, a second bubble of radius '$2R$' is blown. The work required to blow the $2$nd bubble in comparison to that required for the $1$st bubble is

A film of soap is formed between two straight parallel wires of length $10\text{ cm}$ each separated by $0.5\text{ cm}$. If their separation is increased by $1\text{ mm}$ while still maintaining their parallelism. How much work will have to be done?

(surface tension of $= 65 \times 10^{-2}\text{ N/m}$)

A gas is compressed at a constant pressure of $50\text{ N/m}^2$ from a volume of $10\text{ m}^3$ to a volume of $4\text{ m}^3$. Energy of $100\text{ J}$ is then added to the gas by heating. Its internal energy is

A gas at N.T.P. is suddenly compressed to onefourth of its original volume. If $\gamma = 1.5$, then the final pressure is

The side of a copper cube is $1\text{ m}$ at $0^\circ\text{C}$. What will be the change in its volume, when it is heated to $100^\circ\text{C}$? $[\alpha$copper $= 18 \times 10^{-6}/^\circ\text{C}]$

If the length of an open organ pipe is $33.3\text{ cm}$, then the frequency of fifth overtone is [Neglect end correction, velocity of sound $= 333\text{ m/s}$ ]

If the end correction of an open pipe is $0.8\text{ cm}$, then the inner radius of that pipe is

The equation of simple harmonic progressive wave is given by $y = a\sin 2\pi(bt - cx)$. The maximum particle velocity will be half the wave velocity, if $c =$

Stationary waves can be produced in

Light of wavelength ',$\lambda$' is incident on a slit of width '$d$'. The resulting diffraction pattern is observed on a screen at a distance '$D$'. The linear width of the principal maximum is then equal to the width of the slit if $D$ equals

In Young's double slit experiment, the wavelength of light used is '$\lambda$'. The intensity at a point is '$I$' where path difference is $\left(\frac{\lambda}{4}\right)$. If $I_0$ denotes the maximum intensity, then the ratio $\left(\frac{I}{I_0}\right)$ is $\left(\sin \frac{\pi}{4} = \cos \frac{\pi}{4} = \frac{1}{\sqrt{2}}\right)$

In Young's double slit experiment, the fringe width is $2\text{ mm}$. The separation between the $13$th bright fringe and the $4$th dark fringe from the centre of the screen on same side will be