I PUC Physics Question Bank and Study Notes 2026-27

Department of School Education (Pre-University) Administrative Framework

The Government of Karnataka, Department of School Education (Pre University), located at 18th Cross, Malleshwaram, Bengaluru-560012, maintains the official question bank for the I PUC Physics (Subject Code: 33) for the academic year 2026-27. This comprehensive resource is designed for the academic benefit of students and lecturers, aiming to be exhaustive and foolproof. The Director of the Department of School Education (Pre-University) holds the exclusive copyrights. It is strictly for academic purposes and must not be used for commercial gains. No part may be reproduced, stored, or transmitted without prior permission.

I PUC Physics Chapter-Wise Weightage and Marks Allotment

The total teaching duration is $120$ hours, with a total marks allotment of $105$. The maximum marks for the final examination is $70$, out of which the distribution across units and chapters is as follows:

1. Units and Measurements: $3$ teaching hours, $3$ marks.

2. Motion in a Straight Line: $7$ teaching hours, $6$ marks.

3. Motion in a Plane: $13$ teaching hours, $11$ marks.

4. Laws of Motion: $13$ teaching hours, $11$ marks.

5. Work, Energy, and Power: $12$ teaching hours, $10$ marks.

6. System of Particles and Rotational Motion: $11$ teaching hours, $10$ marks.

7. Gravitation: $10$ teaching hours, $9$ marks.

8. Mechanical Properties of Solids: $4$ teaching hours, $4$ marks.

9. Mechanical Properties of Fluids: $5$ teaching hours, $4$ marks.

10. Thermal Properties of Matter: $11$ teaching hours, $10$ marks.

11. Thermodynamics: $8$ teaching hours, $7$ marks.

12. Kinetic Theory of Gases: $5$ teaching hours, $4$ marks.

13. Oscillations: $8$ teaching hours, $7$ marks.

14. Waves: $10$ teaching hours, $9$ marks.

Units and Measurement

Fundamental units are those used for fundamental physical quantities. There are only seven basic quantities, including length, mass, time, temperature, and electric current. Derived quantities are expressed as combinations of these base units. The SI unit of electric current is the ampere ($A$), and the SI unit for the solid angle is the steradian ($sr$). Frequency is measured in hertz ($Hz$), which has the dimensional formula $[M^0L^0T^{-1}]$. Pressure is measured in pascal ($Pa$).

Significant figures adhere to specific rules: all non-zero digits are significant; zeros between non-zero digits are significant; and trailing zeros in a number with a decimal point are significant. However, the power of $10$ is not counted. For example, the number $30600$ has $3$ significant figures, while $0.03400$ has $4$. Dimensional homogeneity states that the dimensions of each term in a physical equation must be the same. Dimensional analysis is used to check the correctness of equations such as $x = v_0t + \frac{1}{2}at^2$ or $T = 2\pi\sqrt{\frac{L}{g}}$. Its limitations include its inability to determine dimensionless constants or handle equations with trigonometric/exponential functions.

Motion in a Straight Line

Distance is a scalar quantity representing the total path length, while displacement is a vector representing the shortest distance between initial and final positions. The numerical ratio of distance to displacement is always greater than or equal to one. Instantaneous velocity is the slope of the tangent to a position-time graph. Acceleration is defined by the slope of a velocity-time graph, while the area under the velocity-time graph represents displacement ($x$).

Kinematic equations for uniform acceleration include: $v = v_0 + at$$x = v_0t + \frac{1}{2}at^2$$v^2 = v_0^2 + 2ax$

For a body thrown vertically upward, the time taken to reach the highest point equals the time taken to return. Acceleration remains downward (due to gravity) throughout the motion. Stopping distance is directly proportional to the square of the initial velocity ($v_0^2$). A body can have constant speed and varying velocity if its direction changes, but it cannot have uniform velocity with varying speed.

Motion in a Plane

Vectors possess both magnitude and direction, unlike scalars which only have magnitude. Two vectors are equal only if they have the same magnitude and same direction. The triangle law of vector addition is used for graphical addition. Centripetal acceleration ($a_c = \frac{v^2}{R}$) is always directed toward the center of the circular path. In uniform circular motion, speed remains constant, but velocity changes due to direction.

Projectile motion is the superposition of two independent motions along perpendicular directions: horizontal motion with constant velocity ($v_x = v_0\cos(\theta)$) and vertical motion with uniform acceleration ($a_y = -g$). The trajectory is a parabola. Relevant formulas include:

1. Time of Flight: $T_f = \frac{2v_0\sin(\theta)}{g}$
2. Maximum Height: $H_m = \frac{v_0^2\sin^2(\theta)}{2g}$
3. Horizontal Range: $R = \frac{v_0^2\sin(2\theta)}{g}$

Maximum range occurs at a projection angle of $45^\circ$, while maximum height occurs at $90^\circ$. Horizontal velocity remains constant throughout the flight. At the maximum height, the velocity is purely horizontal and perpendicular to the acceleration due to gravity.

Laws of Motion

Inertia is the tendency of an object to resist changes in its state of rest or motion; mass is its measure. Newton's First Law defines inertia and force. Newton's Second Law states that force is the rate of change of momentum ($F = \frac{dp}{dt} = ma$). Newton's Third Law states that for every action, there is an equal and opposite reaction; these forces act on different bodies. Momentum ($p = mv$) is conserved in the absence of an external net force, a principle applied in rocket propulsion based on constant momentum change.

Impulse ($I = F\Delta t$) equals the change in momentum. Friction is a contact force opposing relative motion. Static friction ($f_s$) is self-adjusting up to a limiting value, which is proportional to the normal reaction ($N$). Kinetic friction includes sliding and rolling friction, where rolling friction is smaller. On circular roads, banking (tilting the road at an angle $\theta$) provides necessary centripetal force without relying solely on friction. The maximum safe speed on a level road is $v_{max} = \sqrt{\mu_sgR}$, and on a banked road, it is $v_{max} = \sqrt{gR\frac{\mu_s + \tan(\theta)}{1 - \mu_s\tan(\theta)}}$.

Work, Energy, and Power

Work ($W = \vec{F} \cdot \vec{d} = Fd\cos(\theta)$) is the scalar product of force and displacement. No work is done if the force is perpendicular to displacement ($\theta = 90^\circ$) or if displacement is zero. The Work-Energy Theorem states that the work done by a net force equals the change in kinetic energy ($K = \frac{1}{2}mv^2$). Mechanical energy is the sum of kinetic and potential energy. Fore a spring, the potential energy is $V(x) = \frac{1}{2}kx^2$, where $k$ is the spring constant measured in $Nm^{-1}$.

Conservative forces (like gravity and spring force) depend only on initial and final positions, while non-conservative forces (like friction) are path-dependent. In elastic collisions, both linear momentum and kinetic energy are conserved. In perfectly inelastic collisions, bodies stick together after impact ($v = \frac{m_1u_1 + m_2u_2}{m_1 + m_2}$). Power is the rate of doing work ($P = \frac{dW}{dt} = \vec{F} \cdot \vec{v}$), measured in watts ($W$) or horsepower ($1\,hp = 746\,W$).

System of Particles and Rotational Motion

A rigid body maintains constant internal distances under external force. The Center of Mass (CM) of a system moves as if the whole mass is concentrated there. For two particles of masses $m_1$ and $m_2$ at positions $x_1, x_2$, the CM is $X_{cm} = \frac{m_1x_1 + m_2x_2}{m_1 + m_2}$. Rotational variables include torque ($\tau = \vec{r} \times \vec{F}$) and angular momentum ($\vec{L} = \vec{r} \times \vec{p}$). The rotational analogue of Newton's second law is $\tau = I\alpha$ and $\tau = \frac{dL}{dt}$.

Moment of Inertia ($I = \sum m_ir_i^2$) depends on mass distribution and the axis of rotation. Radius of gyration ($k$) is defined by $I = Mk^2$. Angular momentum is conserved ($I\omega = \text{constant}$) if the external torque is zero. A couple consists of two equal and opposite forces with different lines of action, producing rotation without translation. Simple objects' moments of inertia include: circular disc ($\frac{1}{2}MR^2$), hollow cylinder ($MR^2$), and solid sphere ($\frac{2}{5}MR^2$).

Gravitation

Ptolemy proposed the geocentric model, while the heliocentric theory places the Sun at the center. Kepler's three laws characterize planetary motion: the Law of Orbits (elliptical paths), the Law of Areas (constant areal velocity, signifying constant angular momentum), and the Law of Periods ($T^2 \propto R^3$). Newton's Universal Law of Gravitation states $F = G\frac{m_1m_2}{r^2}$. The universal gravitational constant $G = 6.67 \times 10^{-11}\,Nm^2kg^{-2}$.

Acceleration due to gravity ($g$) at Earth's surface is approximately $9.8\,m/s^2$. It decreases with both height ($h$) and depth ($d$). Formulas for variation are $g(h) = g(1 - \frac{2h}{R})$ (for $h \ll R$) and $g(d) = g(1 - \frac{d}{R})$. Escape speed is the minimum speed needed to leave Earth's gravitational influence, calculated as $v_e = \sqrt{\frac{2GM}{R}} = 11.2\,km/s$. For satellites, orbital speed is $v_o = \sqrt{\frac{GM}{R+h}}$. Total energy of an orbiting satellite is negative, indicating it is bound to Earth.

Mechanical Properties of Solids

Stress is restoring force per unit area ($Pa$), and strain is fractional change in dimension. Hooke's Law states stress is proportional to strain within the elastic limit. Moduli of elasticity include Young’s modulus ($Y$) for length, Rigidity modulus ($G$) for shape, and Bulk modulus ($B$) for volume. The ratio of lateral strain to longitudinal strain is Poisson's ratio ($\sigma$). Compressibility is the reciprocal of the Bulk modulus ($1/B$).

In a stress-strain curve, the yield point marks the start of plastic deformation, and the ultimate tensile strength is the maximum stress before necking occurs. Steel is more elastic than rubber because it requires more stress for the same strain ($Y_{steel} > Y_{rubber}$). Beams with an I-section are used in structural design to prevent buckling and maximize strength with less weight. The elastic energy density in a stretched wire is $u = \frac{1}{2}\sigma\epsilon$.

Mechanical Properties of Fluids

Fluids include liquids and gases. Pascal's Law states that pressure applied to an enclosed fluid is transmitted undiminished throughout. This is used in hydraulic lifts. Gauge pressure is the difference between absolute and atmospheric pressure ($P - P_a = h\rho g$). The continuity equation states $Av = \text{constant}$, enforcing mass conservation in flow. Bernoulli’s principle relates pressure, velocity, and height: $P + \frac{1}{2}\rho v^2 + \rho gh = \text{constant}$.

Viscosity is internal fluid friction. Stoke’s Law gives the drag force on a sphere ($F = 6\pi\eta rv$), leading to terminal velocity. Surface tension ($S = F/L$) causes liquid drops to be spherical ($P_{excess} = 2S/r$) and is responsible for capillary rise ($h = \frac{2S\cos(\theta)}{r\rho g}$). Detergents reduce surface tension to act as wetting agents. The Magnus effect explains the dynamic lift on spinning objects.

Thermal Properties of Matter

Temperature is measured on Celsius, Fahrenheit, and Kelvin scales; they relate as $T_C = \frac{5}{9}(T_F - 32)$. Absolute zero is $0\,K$ or $-273.15^\circ C$. Thermal expansion includes linear ($\alpha_L$), area ($\alpha_A$), and volume ($\alpha_V$) expansion, related by $\alpha_L : \alpha_A : \alpha_V = 1 : 2 : 3$. Water exhibits anomalous expansion, reaching maximum density at $4^\circ C$.

Specific heat capacity ($c$) is the heat required to raise the temperature of a unit mass by one degree. Latent heat is heat absorbed/released during phase changes without temperature change. Heat transfer occurs via conduction (through solids), convection (through fluid motion), and radiation (fastest mode, via electromagnetic waves). Stefan-Boltzmann Law states $E = \sigma T^4$, and Wein’s Displacement Law states $\lambda_m T = \text{constant}$. Newton's Law of Cooling states the rate of heat loss is proportional to the temperature difference between the body and surroundings.

Thermodynamics

The Zeroth Law of Thermodynamics defines temperature and equilibrium. The First Law is the conservation of energy: $\Delta Q = \Delta U + \Delta W$. Internal energy of an ideal gas depends solely on temperature. Thermodynamic processes include Isothermal ($T$ constant, $\Delta U=0$), Adiabatic ($\Delta Q=0$), Isobaric ($P$ constant), and Isochoric ($V$ constant, $\Delta W=0$).

Work done by a gas in an isothermal expansion from $V_1$ to $V_2$ is $W = 2.303\mu RT \log_{10}(\frac{V_2}{V_1})$. For adiabatic processes, $PV^\gamma = \text{constant}$. The Second Law (Kelvin-Planck/Clausius) restricts heat flow and efficiency. The Carnot engine is a theoretical reversible heat engine with efficiency $\eta = 1 - \frac{T_2}{T_1}$. A Carnot cycle consists of four stages: isothermal expansion, adiabatic expansion, isothermal compression, and adiabatic compression.

Kinetic Theory of Gases

Real gases behave like ideal gases at high temperature and low pressure. The ideal gas equation is $PV = \mu RT = Nk_BT$. Postulates of kinetic theory assume gases consist of molecules in random motion undergoing elastic collisions. Pressure is given by $P = \frac{1}{3}nm\bar{v}^2$. Root mean square (rms) speed is $v_{rms} = \sqrt{\frac{3k_BT}{m}}$, proportional to $\sqrt{T}$.

The law of equipartition of energy states that in equilibrium, each degree of freedom contributes $\frac{1}{2}k_BT$ average energy. A monoatomic gas has $3$ degrees of freedom, while a rigid diatomic gas has $5$. Mean free path is the average distance between collisions. For solids, specific heat capacity approaches $3R$. Specific heat ratio ($\gamma = C_p/C_v$) for a monoatomic gas is $5/3$.

Oscillations

Periodic motion repeats at regular intervals; oscillatory motion is to-and-fro motion about an equilibrium. Simple Harmonic Motion (SHM) is characterized by a restoring force proportional to displacement ($F = -kx$). Displacement is expressed as $x(t) = A\cos(\omega t + \phi)$. Velocity ($v$) is maximum at the mean position ($v_{max} = A\omega$), while acceleration ($a$) is maximum at extreme positions ($a_{max} = \omega^2A$).

Total mechanical energy in SHM ($E = \frac{1}{2}kA^2$) is conserved, fluctuating between kinetic and potential. For a simple pendulum, the period is $T = 2\pi\sqrt{\frac{L}{g}}$. A second's pendulum has a period of $2\,s$ and a length of approx $1\,m$. For a spring-mass system, $T = 2\pi\sqrt{\frac{m}{k}}$. Frequency is the reciprocal of the time period ($\nu = 1/T$).

Waves

Mechanical waves (like sound) require a medium, whereas electromagnetic waves (like light) travel through a vacuum. Transverse waves involve particle motion perpendicular to wave travel (crests/troughs) and propagate only in solids/surfaces. Longitudinal waves involve motion parallel to wave travel (compressions/rarefactions) and propagate in all media. Velocity of sound in gas is given by $v = \sqrt{\frac{\gamma P}{\rho}}$, known as the Laplace correction to Newton's formula.

Stationary waves are formed by the interference of two identical waves traveling in opposite directions; they do not carry energy. Nodes have zero amplitude, while antinodes have maximum amplitude. In pipes, open pipes support all harmonics, while closed pipes support only odd harmonics. Beats are produced by sources with slightly different frequencies ($\nu_b = |\nu_1 - \nu_2|$). Velocity of a transverse wave on a stretched string depends on tension ($T$) and linear mass density ($\mu$): $v = \sqrt{T/\mu}$.

Development and Scrutiny Committees (2026-27)

Development Committee:

• Mahesh B (Coordinator): Principal, Government PU College, Mylanayakanahosahalli, Ramanagara Dist.
• Adithya Rao K V (Member): Lecturer, Government PU College, Sringeri, Chikmagalur Dist.
• Prakash N (Member): Lecturer, Govt. PU College for Girls, Chennapatna, Ramanagara Dist.
• Devaraj Talakallu (Member): Lecturer, Govt. Science PU College, Dastikoppa, Dharwad Dist.

Scrutiny Committee:

• Shreenivasa M Bhat: Lecturer, Government PU College, Karwar, Uttara Kannada Dist.
• Ganesh: Lecturer, GPU College (Ex-Municipal), Mandya, Mandya Dist.

Preparation Committee (2024-25 Archive):

• Mahesh B, Adithya Rao K V, Prasanna K V, Prakash N, Devaraj Talakallu, Mahesh, and Chethana.