Maharashtra Board Class 12 Physics Question Paper 2023 with Answer Key (February 27)

i. If ‘n’ is the number of molecules per unit volume and ‘d’ is the diameter of the molecules, the mean free path ‘λ’ of molecules is:

• (1) \( \pi n d^2 \)
• (2) \( \frac{1}{2 \pi n d^2} \)
• (3) \( \frac{1}{\sqrt{2} \pi n d^2} \)
• (4) \( \frac{1}{\pi n d^2} \)

ii. The first law of thermodynamics is consistent with the law of conservation of _______.

• (1) momentum
• (2) energy
• (3) mass
• (4) velocity

iii. \( Y = A + B \) is the Boolean expression for _______.

• (1) OR - gate
• (2) AND - gate
• (3) NOR - gate
• (4) NAND - gate

iv. The property of light which remains unchanged when it travels from one medium to another is _______.

• (1) velocity
• (2) wavelength
• (3) amplitude
• (4) frequency

v. If a circular coil of 100 turns with a cross-sectional area of 1 m\(^2\) is kept with its plane perpendicular to a magnetic field of 1 T, the magnetic flux linked with the coil will be _______.

• (1) 1 Wb
• (2) 50 Wb
• (3) 100 Wb
• (4) 200 Wb

vi. If ‘θ’ represents the angle of contact made by a liquid which completely wets the surface of the container, then _______.

• (1) \( \theta = 0 \)
• (2) \( 0 < \theta < \frac{\pi}{2} \)
• (3) \( \theta = \frac{\pi}{2} \)
• (4) \( \frac{\pi}{2} < \theta < \pi \)

vii. The LED emits visible light when its _______.

• (1) junction is reverse biased
• (2) depletion region widens
• (3) holes and electrons recombine
• (4) junction becomes hot

viii. Soft iron is used to make the core of a transformer because of its _______.

• (1) low coercivity and low retentivity
• (2) low coercivity and high retentivity
• (3) high coercivity and high retentivity
• (4) high coercivity and low retentivity

ix. If the maximum kinetic energy of emitted electrons in the photoelectric effect is 2 eV, the stopping potential will be _______.

• (1) 0.5 V
• (2) 1.0 V
• (3) 1.5 V
• (4) 2.0 V

x. The radius of the eighth orbit of the electron in the H-atom will be more than that of the fourth orbit by a factor of _______.

• (1) 2
• (2) 4
• (3) 8
• (4) 16

i. What is the value of resistance for an ideal voltmeter?

ii. What is the value of force on a closed circuit in a magnetic field?

iii. What is the average value of alternating current over a complete cycle?

iv. An electron is accelerated through a potential difference of 100 volt. Calculate de-Broglie wavelength in nm.

v. If friction is made zero for a road, can a vehicle move safely on this road?

vi. State the formula giving relation between electric field intensity and potential gradient.

vii. Calculate the velocity of a particle performing S.H.M. after 1 second, if its displacement is \( x = 5 \sin \left( \frac{\pi}{3} t \right) \) m.

viii. Write the mathematical formula for Bohr magneton for an electron revolving in nth orbit.

Define coefficient of viscosity. State its formula and S.I. units.

Obtain an expression for magnetic induction of a toroid of ‘N’ turns about an axis passing through its centre and perpendicular to its plane.

State and prove the principle of conservation of angular momentum.

Obtain an expression for equivalent capacitance of two capacitors \( C_1 \) and \( C_2 \) connected in series.

Explain why the equivalent inductance of two coils connected in parallel is less than the inductance of either of the coils.

How will you convert a moving coil galvanometer into an ammeter?

A 100 Ω resistor is connected to a 220 V, 50 Hz supply. Calculate:

i. r.m.s. value of current

ii. net power consumed over the full cycle

A bar magnet of mass 120 g in the form of a rectangular parallelepiped, has dimensions \( l = 40 \, mm \), \( b = 100 \, mm \), and \( h = 80 \, mm \), with its dimension ‘h’ vertical, the magnet performs angular oscillations in the plane of the magnetic field with period \( \pi \) seconds. If the magnetic moment is 3.4 Am\(^2\), determine the influencing magnetic field.

Distinguish between free vibrations and forced vibrations (Two points).

Compare the rate of loss of heat from a metal sphere at 827°C with rate of loss of heat from the same at 427°C, if the temperature of surrounding is 27°C.

An ideal mono-atomic gas is adiabatically compressed so that its final temperature is twice its initial temperature. Calculate the ratio of final pressure to its initial pressure.

Disintegration rate of a radio-active sample is 10\(^{10}\) per hour at 20 hours from the start. It reduces to 5 \(\times\) 10\(^9\) per hour after 30 hours. Calculate the decay constant.

Derive laws of reflection of light using Huygens’ principle.

State postulates of Bohr’s atomic model.

Define and state unit and dimensions of:

(i) Magnetization

(ii) Magnetic susceptibility

With neat labelled circuit diagram, describe an experiment to study the characteristics of photoelectric effect.

Explain the use of potentiometer to determine internal resistance of a cell.

Explain the working of n-p-n transistor in common base configuration.

State the differential equation of linear S.H.M. Hence, obtain expression for:

(i) acceleration

(ii) velocity

Two tuning forks of frequencies 320 Hz and 340 Hz are sounded together to produce sound wave. The velocity of sound in air is 326.4 m/s. Calculate the difference in wavelengths of these waves.

In a biprism experiment, the fringes are observed in the focal plane of the eye-piece at a distance of 1.2 m from the slit. The distance between the central bright band and the 20th bright band is 0.4 cm. When a convex lens is placed between the biprism and the eye-piece, 90 cm from the eye-piece, the distance between the two virtual magnified images is found to be 0.9 cm. Determine the wavelength of light used.

Calculate the current flowing through two long parallel wires carrying equal currents and separated by a distance of 1.35 cm experiencing a force per unit length of 4.76 × 10^-2 N/m.

An alternating voltage given by e = 140 sin (314.2 t) is connected across a pure resistor of 50 Ω. Calculate:

(i) the frequency of the source

(ii) the r.m.s current through the resistor

An electric dipole consists of two opposite charges each of magnitude 1 μC, separated by 2 cm. The dipole is placed in an external electric field of 10^5 N/C. Calculate the:

i. maximum torque experienced by the dipole and

ii. work done by the external field to turn the dipole through 180°.

On the basis of kinetic theory of gases obtain an expression for pressure exerted by gas molecules enclosed in a container on its walls.

i. Derive an expression for energy stored in the magnetic field in terms of induced current.

ii. A wire 5 m long is supported horizontally at a height of 15 m along east-west direction. When it is about to hit the ground, calculate the average e.m.f. induced in it. (g = 10 m/s²)

i. Derive an expression for the work done during an isothermal process.

ii. 10⁴ J of work is done on certain volume of a gas. If the gas releases 125 kJ of heat, calculate the change in internal energy of the gas.

i. Obtain the relation between surface energy and surface tension.

ii. Calculate the work done in blowing a soap bubble to a radius of 1 cm. The surface tension of soap solution is 2.5 × 10^-2 N/m.

Derive expressions for linear velocity at lowest position, mid-way position and the top-most position for a particle revolving in a vertical circle, if it has to just complete circular motion without string slackening at top.