Semester 1 Physics - West Bengal Board Physics

Physics: Key MCQ Concepts and Formulas for Class 11 Semester 1

Physical Quantities, Units, and Measurement

Physical quantities are measured using standard units. The transcript emphasizes the importance of knowing which units correspond to which physical quantities and the dimensional analysis of equations. The steradian is highlighted as the unit of solid angle.

• Steradian: Unit of solid angle (solid angle = steradian).
• Dimensional Analysis: When adding or subtracting terms in an equation, their dimensions must be the same.
• Vernier Caliper: Least count formula: $LC = 1 \text{ MSD} - 1 \text{ VSD}$.
• Significant Figures:…

Physics: Key MCQ Concepts and Formulas for Class 11 Semester 1

Physical Quantities, Units, and Measurement

Physical quantities are measured using standard units. The transcript emphasizes the importance of knowing which units correspond to which physical quantities and the dimensional analysis of equations. The steradian is highlighted as the unit of solid angle.

• Steradian: Unit of solid angle (solid angle = steradian).
• Dimensional Analysis: When adding or subtracting terms in an equation, their dimensions must be the same.
• Vernier Caliper: Least count formula: $LC = 1 \text{ MSD} - 1 \text{ VSD}$.
• Significant Figures: Zeros between nonzero digits are significant; leading zeros are not. Trailing zeros after a decimal are significant.

Dimensional Analysis and Error Calculation

Dimensional analysis is used to check the correctness of equations and to derive relationships between physical quantities. Error calculation is crucial for determining the accuracy of measurements.

• Dimensional Formula for Pressure: $[M L^{-1} T^{-2}]$.
• Error Propagation: For a quantity $Q = a^p b^q / c^r$, the relative error is:$$\frac{\Delta Q}{Q} = p \frac{\Delta a}{a} + q \frac{\Delta b}{b} + r \frac{\Delta c}{c}$$
• Percentage Error: Always add the absolute values of individual percentage errors; errors do not subtract.

Motion in One Dimension

Motion in a straight line involves concepts of displacement, velocity, acceleration, and their interrelations. The transcript covers average velocity, differentiation for velocity and acceleration, and the use of kinematic equations.

• Average Velocity (Equal Distances, Different Speeds):$$v_{avg} = \frac{2 v_1 v_2}{v_1 + v_2}$$
• Differentiation: Velocity is the derivative of displacement with respect to time; acceleration is the derivative of velocity.
• Kinematic Equation: $x = ut + \frac{1}{2} a t^2$.

Graphical Analysis of Motion

Graphs are used to interpret and analyze motion. The transcript discusses velocity-time and acceleration-time graphs, and how to deduce motion characteristics from them.

• Area under $v$-$t$ graph: Displacement.
• Slope of $v$-$t$ graph: Acceleration.
• Impossible $v$-$t$ graph: At a given instant, velocity cannot have two different values.

Vectors and Vector Operations

Vectors are quantities with both magnitude and direction. The transcript covers unit vectors, vector addition, dot and cross products, and projection of one vector onto another.

• Unit Vector: For vector $\vec{A}$, unit vector $\hat{A} = \vec{A} / |\vec{A}|$.
• Projection of $\vec{A}$ on $\vec{B}$: $A \cos \theta = \frac{\vec{A} \cdot \vec{B}}{|\vec{B}|}$.
• Dot Product: $\vec{A} \cdot \vec{B} = AB \cos \theta$.
• Cross Product: $|\vec{A} \times \vec{B}| = AB \sin \theta$.
• Resultant of Two Equal Vectors at Angle $\theta$: $2A \cos(\theta/2)$.

Projectile Motion

Projectile motion involves two-dimensional motion under gravity. The transcript details the conditions for equal range, velocity and acceleration components, and energy at the highest point.

• Complementary Angles for Equal Range: If a projectile is thrown at angles $\alpha$ and $90^\circ - \alpha$, the range is the same.
• Horizontal Velocity Component: Remains constant throughout the motion.
• Vertical Velocity Component: Changes due to gravity.
• Maximum Height: $H_{max} = \frac{u^2 \sin^2 \theta}{2g}$
• Range: $R = \frac{u^2 \sin 2\theta}{g}$
• Kinetic Energy at Highest Point: $KE_{max} = \frac{1}{2} m u^2 \cos^2 \theta$
• Ratio of Kinetic to Potential Energy at Highest Point: $\cot^2 \theta$

Laws of Motion and Friction

Newton’s laws govern the motion of objects. The transcript covers tension in strings, pulley systems, friction, and pseudo forces in non-inertial frames.

• Tension in String (Pulley System): For masses $m_1$ and $m_2$,$$a = \frac{(m_2 - m_1)g}{m_1 + m_2}$$$$T = \frac{2 m_1 m_2 g}{m_1 + m_2}$$
• Friction on Inclined Plane: For equilibrium, $mg \sin \alpha = \mu mg \cos \alpha \implies \mu = \tan \alpha$.
• Pseudo Force: In an accelerating frame, $F_{pseudo} = -ma$ acts opposite to the acceleration of the frame.
• Angle of Inclination for Block to Remain Stationary: $a = g \tan \alpha$

Work, Energy, and Power

Work is done when a force causes displacement. The transcript discusses calculation of work using dot product, kinetic energy changes, and energy conservation in various systems.

• Work Done by Force $\vec{F}$ over Displacement $\vec{S}$: $W = \vec{F} \cdot \vec{S}$
• Change in Kinetic Energy: $W = \Delta KE = \frac{1}{2} m v^2 - \frac{1}{2} m u^2$
• Work in Variable Force: Integrate force over displacement.
• Conservation of Energy in Circular Motion: $mgh = \frac{1}{2} m v^2$ at the bottom of a smooth curve.

Circular and Rotational Motion

Circular motion involves movement along a circular path. The transcript covers angular velocity, centripetal acceleration, and conservation of angular momentum.

• Centripetal Acceleration: $a_c = \frac{v^2}{r}$
• Angular Displacement: $\theta = \omega t + \frac{1}{2} \alpha t^2$
• Conservation of Angular Momentum: $I_1 \omega_1 + I_2 \omega_2 = (I_1 + I_2) \omega_f$
• Rotational Kinetic Energy: $KE = \frac{1}{2} I \omega^2$
• Loss of Kinetic Energy on Combining Rotating Bodies:$$\Delta KE = \frac{1}{2} I (\omega_1^2 + \omega_2^2) - \frac{1}{2} (2I) \left( \frac{\omega_1 + \omega_2}{2} \right)^2 = \frac{I}{4} (\omega_1 - \omega_2)^2$$

Error Analysis and Significant Figures

Accurate measurement and reporting require understanding of errors and significant figures. The transcript provides rules for counting significant digits and propagating errors.

• Counting Significant Figures:
  • All nonzero digits are significant.
  • Zeros between nonzero digits are significant.
  • Leading zeros are not significant.
  • Trailing zeros after a decimal point are significant.
• Error Propagation in Multiplication/Division: Add relative errors.
• Error Propagation in Addition/Subtraction: Add absolute errors.

Key Problem-Solving Strategies and Common Pitfalls

The transcript emphasizes careful reading of questions, correct application of formulas, and awareness of common mistakes, especially in dimensional analysis, vector operations, and error calculation.

• Always check units and dimensions before finalizing an answer.
• In error calculation, never subtract errors; always add their absolute values.
• For vector projections, use the correct formula for the required direction.
• In projectile motion, remember which velocity component remains constant.
• In friction problems, identify the direction of friction and normal reaction correctly.
• For pulley and tension problems, use the net force and total mass approach for acceleration.
• In rotational motion, apply conservation of angular momentum when no external torque acts.

These points summarize the high-yield concepts, formulas, and problem-solving approaches explicitly covered, focusing on exam-relevant recall and application.