JEE Main Physics Flashcards

24 sample cards from the Physics deck

Sampled from the end of the deck, so these are different cards from the ones shown on the syllabus page.

1. State the principle of homogeneity of dimensions.

   In a physically correct equation, every term on both sides must have the same dimensions; only quantities of identical dimensions can be added, subtracted or equated.

2. Give one example each of a dimensionless quantity and a dimensionless quantity that still has a unit.

   Dimensionless without unit: strain (ratio of lengths) or refractive index. Dimensionless but with a unit: plane angle (radian) and solid angle (steradian).

3. List the three main uses (applications) of dimensional analysis.

   1) Checking the dimensional correctness of an equation (homogeneity). 2) Deriving the relation among physical quantities. 3) Converting a unit from one system to another.

4. State two important limitations of dimensional analysis.

   It cannot determine dimensionless constants (like $\frac{1}{2}$ or $2\pi$), and it cannot derive relations involving more than three unknowns, trigonometric, exponential or logarithmic functions, or sums of terms.

5. Using dimensional analysis, give the formula to convert the numerical value of a quantity between unit systems.

   $n_2 = n_1 \left[\dfrac{M_1}{M_2}\right]^{a}\left[\dfrac{L_1}{L_2}\right]^{b}\left[\dfrac{T_1}{T_2}\right]^{c}$, where $a,b,c$ are the dimensions of mass, length and time in the quantity.

6. What is a frame of reference?

   A frame of reference is a coordinate system (with an origin and axes) attached to an observer, together with a clock, used to specify the position and time of events; motion is always described relative to it.

7. Distinguish inertial and non-inertial frames of reference.

   An inertial frame is one moving with constant velocity (zero acceleration) in which Newton's first law holds. A non-inertial frame is accelerating, requiring pseudo (fictitious) forces to apply Newton's laws.

8. What does 'motion in a straight line' (rectilinear motion) mean, and is it one-dimensional?

   It is motion of an object along a single straight-line path, so it is one-dimensional motion; position can be specified by a single coordinate $x$ along that line.

9. Distinguish distance and displacement.

   Distance is the total path length travelled (scalar, always positive). Displacement is the shortest straight-line vector from initial to final position (vector, can be positive, negative or zero). $|\text{displacement}| \leq \text{distance}$.

10. What information is given by the slope of a position–time graph?

    The slope of a position–time ($x$–$t$) graph gives the velocity: $v = \dfrac{dx}{dt}$. A steeper slope means greater speed; a horizontal line means the object is at rest.

11. How do you read the position–time graphs for an object at rest, in uniform motion, and in accelerated motion?

    At rest: a horizontal straight line. Uniform motion: a sloping straight line (constant slope). Accelerated motion: a curved line (changing slope).

12. Define speed and velocity and state which is scalar and which is vector.

    Speed is the rate of change of distance, $\text{speed} = \frac{\text{distance}}{\text{time}}$, a scalar. Velocity is the rate of change of displacement, $\vec{v} = \frac{\Delta \vec{x}}{\Delta t}$, a vector.

13. Distinguish uniform and non-uniform motion.

    In uniform motion the object covers equal displacements in equal intervals of time (constant velocity, zero acceleration). In non-uniform motion it covers unequal displacements in equal time intervals (velocity changes, so acceleration is non-zero).

14. Define average speed and average velocity.

    Average speed $= \dfrac{\text{total distance}}{\text{total time}}$ (scalar). Average velocity $\vec{v}_{avg} = \dfrac{\Delta \vec{x}}{\Delta t} = \dfrac{x_2 - x_1}{t_2 - t_1}$ (vector).

15. For a body covering equal distances at speeds $v_1$ and $v_2$, what is the average speed?

    The average speed is the harmonic mean: $v_{avg} = \dfrac{2 v_1 v_2}{v_1 + v_2}$.

16. Define instantaneous velocity and instantaneous speed.

    Instantaneous velocity is the velocity at a particular instant: $\vec{v} = \lim_{\Delta t \to 0}\dfrac{\Delta \vec{x}}{\Delta t} = \dfrac{d\vec{x}}{dt}$. Instantaneous speed is its magnitude, $|\vec{v}|$.

17. Define average and instantaneous acceleration.

    Average acceleration $\vec{a}_{avg} = \dfrac{\Delta \vec{v}}{\Delta t}$. Instantaneous acceleration $\vec{a} = \lim_{\Delta t \to 0}\dfrac{\Delta \vec{v}}{\Delta t} = \dfrac{d\vec{v}}{dt} = \dfrac{d^{2}x}{dt^{2}}$. SI unit: $\text{m}\,\text{s}^{-2}$.

18. What is uniformly accelerated motion?

    Motion in which the velocity changes by equal amounts in equal intervals of time, i.e. the acceleration is constant in both magnitude and direction (e.g. free fall under gravity).

19. Write the three equations of motion for uniformly accelerated motion.

    $v = u + at$; $\;s = ut + \frac{1}{2}at^{2}$; $\;v^{2} = u^{2} + 2as$, where $u$ is initial velocity, $v$ final velocity, $a$ constant acceleration, $s$ displacement and $t$ time.

20. Give the formula for the displacement in the $n$-th second of uniformly accelerated motion.

    $s_{n} = u + \dfrac{a}{2}(2n - 1)$ — the displacement during the $n$-th second only (not the total distance up to $n$ seconds).

21. What does the slope of a velocity–time graph represent, and what does the area under it represent?

    The slope of a velocity–time graph gives acceleration, $a = \dfrac{dv}{dt}$. The area under the $v$–$t$ graph gives the displacement of the object.

22. Describe the velocity–time graph for uniform velocity and for uniform acceleration starting from rest.

    Uniform velocity: a horizontal straight line parallel to the time axis. Uniform acceleration from rest: a straight line through the origin with positive constant slope.

23. How is displacement found from a velocity–time graph for uniformly accelerated motion (graphical derivation idea)?

    The displacement equals the area of the trapezium under the $v$–$t$ line: $s = \frac{1}{2}(u + v)t$, the area combining the rectangle ($ut$) and triangle ($\frac{1}{2}at^{2}$).

24. What does a negative slope (downward line) on a velocity–time graph indicate?

    A negative slope indicates negative acceleration (retardation/deceleration); the magnitude of velocity is decreasing with time while the object may still be moving in the positive direction.

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