Every year NEET asks two to four questions that come straight from the laboratory: reading a vernier scale, spotting a zero error, deciding which quantity contributes most to the error in a formula, or identifying a circuit component from a symbol. These are among the cheapest marks in the paper because the reasoning is short and the same handful of instruments and formulas repeat.
Least Count, Zero Error and Reading Instruments
Every measuring device has a least count (LC) — the smallest change in the measured quantity it can register. For scale-plus-auxiliary-scale instruments:
$$\text{LC} = \frac{\text{value of 1 main scale division}}{\text{number of divisions on the auxiliary scale}}$$
Vernier callipers. A vernier scale of $n$ divisions is cut so that it spans $(n-1)$ main scale divisions. Hence LC = 1 MSD − 1 VSD = 1 MSD/$n$. For the standard instrument, 1 MSD = 1 mm and $n$ = 10, giving LC = 0.1 mm = 0.01 cm.
Reading = (main scale reading just before the vernier zero) + (number of the vernier division that coincides best with a main scale line) × LC.
Screw gauge (micrometer). Here LC = pitch / number of circular scale divisions. Pitch is the axial distance the spindle advances per full rotation; if the spindle moves 1 mm in 2 rotations, pitch = 0.5 mm, and with 50 circular divisions LC = 0.01 mm. Reading = linear (pitch) scale reading + circular scale division × LC.
Zero error. Close the jaws (or bring the screw faces into contact). If the reading is not zero, the instrument has a zero error, and
$$\text{Correct reading} = \text{observed reading} - \text{zero error (with its sign)}$$
- Positive zero error: the vernier/circular zero lies ahead of the main scale zero. Subtract it.
- Negative zero error: the vernier/circular zero lies behind the main scale zero. Its magnitude is $(n - x)\times$LC, where $x$ is the coinciding division; subtracting a negative error means adding.
Spherometer, used for radius of curvature of a spherical surface, works on the same screw principle:
$$R = \frac{l^{2}}{6h} + \frac{h}{2}$$
where $h$ is the sagitta (elevation/depression) and $l$ the mean distance between the legs.
Error propagation decides which measurement to make carefully. For $Z = A^{p}B^{q}/C^{r}$,
$$\frac{\Delta Z}{Z} = p\frac{\Delta A}{A} + q\frac{\Delta B}{B} + r\frac{\Delta C}{C}$$
So the quantity raised to the highest power, measured with the fewest significant figures, dominates the error — a favourite question type.
Mechanics Experiments
Simple pendulum. For small amplitude, $T = 2\pi\sqrt{L/g}$, so
$$g = \frac{4\pi^{2}L}{T^{2}}$$
The effective length $L$ = length of thread + radius of the bob. A graph of $T^{2}$ against $L$ is a straight line through the origin with slope $4\pi^{2}/g$. Time 20–50 oscillations and divide, because the fractional error in $T$ falls as the number of oscillations rises. Since $g \propto 1/T^{2}$, the error in the time period counts double.
Young's modulus by Searle's apparatus. A wire of length $L$ and radius $r$ carrying load $Mg$ elongates by $\ell$:
$$Y = \frac{Mg L}{\pi r^{2}\ell}$$
The radius is measured with a screw gauge and appears squared, so it is usually the largest error contributor; $\ell$ is read with a micrometer-fitted vernier.
Surface tension by capillary rise.
$$T = \frac{r h \rho g}{2\cos\theta}$$
For water in clean glass $\theta \approx 0$, so $T = rh\rho g/2$. Narrower tube → greater rise; note that $rh$ is constant for a given liquid. The same concept explains why the meniscus is concave for wetting liquids and convex for mercury.
Viscosity by terminal velocity. A sphere of radius $r$ and density $\sigma$ falling through a liquid of density $\rho$ reaches
$$v_{t} = \frac{2r^{2}(\sigma-\rho)g}{9\eta}$$
Measure the time to cross a known length in the uniform-velocity region, well below the surface.
Others in this group: verification of the parallelogram law with a Gravesand apparatus, determination of the coefficient of friction on an inclined plane ($\mu = \tan\theta$ at the angle of repose), and the moment-of-inertia/torque type experiments with a metre scale balanced on a wedge.
Heat and Sound Experiments
Specific heat capacity by the method of mixtures. Using a calorimeter (water equivalent $W$), heat lost by the hot body equals heat gained:
$$m_{1}c_{1}(\theta_{1}-\theta) = (m_{2}c_{2} + W)(\theta - \theta_{2})$$
For latent heat of fusion of ice, the extra term $mL$ appears. Sources of error: radiation loss, stirring, and heat retained by the thermometer.
Newton's law of cooling. The rate of fall of temperature is proportional to the excess over the surroundings; plotting temperature against time gives an exponential decay, while $\log(\theta-\theta_{0})$ against $t$ is a straight line with negative slope.
Speed of sound by resonance tube. For a tube closed at one end and open at the other, resonance occurs at lengths $\ell_1$ (first) and $\ell_2$ (second) with
$$v = 2f(\ell_{2}-\ell_{1})$$
This elegantly cancels the end correction $e$, since $\ell_1 + e = \lambda/4$ and $\ell_2 + e = 3\lambda/4$. Separately, $e = (\ell_{2}-3\ell_{1})/2 \approx 0.6r$. The room temperature must be noted because $v \propto \sqrt{T}$ (about 0.61 m/s rise per °C near 0 °C, with $v \approx 332$ m/s at 0 °C).
Electricity and Magnetism Experiments
Ohm's law and resistivity. Plot $V$ against $I$ for a metallic conductor: a straight line whose slope gives $R$. Then
$$\rho = \frac{RA}{L} = \frac{R\pi d^{2}}{4L}$$
with $d$ measured by screw gauge.
Metre bridge (a practical Wheatstone bridge). At balance, with the jockey at length $\ell$ cm from the left end,
$$\frac{R}{S} = \frac{\ell}{100-\ell}$$
Keep the balance point near the middle of the wire (roughly 40–60 cm) — that is where the fractional error in $R$ is least. Interchange $R$ and $S$ and average to eliminate end resistances.
Potentiometer. The working principle is that the potential drop along a uniform wire is proportional to its length: $V = \phi\ell$, where $\phi$ is the potential gradient. Uses:
- Comparing two emfs: $E_{1}/E_{2} = \ell_{1}/\ell_{2}$.
- Internal resistance of a cell: $r = R\left(\dfrac{\ell_{1}-\ell_{2}}{\ell_{2}}\right)$, where $\ell_1$ is the balancing length with the cell open-circuited and $\ell_2$ with shunt $R$ across it.
The driver cell's emf must exceed the emf being measured, and the positive terminals of both cells must be joined to the same end of the wire — otherwise no null point exists anywhere.
Meters and galvanometers. A galvanometer of resistance $G$ and full-scale current $I_g$ becomes:
- an ammeter of range $I$ by a parallel shunt $S = \dfrac{I_{g}G}{I-I_{g}}$ (ideal ammeter: zero resistance, in series),
- a voltmeter of range $V$ by a series resistance $R = \dfrac{V}{I_{g}} - G$ (ideal voltmeter: infinite resistance, in parallel).
Also expected: resistance and figure of merit of a galvanometer by the half-deflection method, $G = \dfrac{R S}{R-S}$ and figure of merit $k = \dfrac{E}{(R+G)\theta}$; and the use of a magnetic needle/tangent galvanometer type arrangement where $\tan\theta \propto B$.
Optics and Electronics
Refractive index. Using a glass slab and pins, real depth/apparent depth gives $n$; using a prism, plot the deviation $\delta$ against the angle of incidence $i$ — the curve is U-shaped with a minimum, and
$$n = \frac{\sin\left(\frac{A+\delta_{m}}{2}\right)}{\sin(A/2)}$$
Note the $i$–$\delta$ graph is not symmetric-looking near the ends, but two incidence angles give the same deviation.
Focal length. For a convex lens or concave mirror, use $\dfrac{1}{v} - \dfrac{1}{u} = \dfrac{1}{f}$ (lens) or $\dfrac{1}{v} + \dfrac{1}{u} = \dfrac{1}{f}$ (mirror) with the Cartesian sign convention. A $1/v$ versus $1/u$ plot is linear with intercepts of magnitude $1/f$ on both axes. Parallax between the object pin and the image is removed by moving the eye sideways. A concave lens's focal length is found in combination with a convex lens: $\dfrac{1}{F} = \dfrac{1}{f_{1}} + \dfrac{1}{f_{2}}$.
p–n junction diode characteristics. Forward bias: current stays nearly zero until the knee (about 0.3 V for germanium, 0.7 V for silicon), then rises steeply — so use a series resistor to limit current, a low-range voltmeter and a milliammeter. Reverse bias: only a microampere-level saturation current flows until breakdown. A Zener diode is operated in reverse breakdown, where voltage stays constant — the basis of voltage regulation. An LED is a forward-biased diode that emits light.
Transistor characteristics (common-emitter n-p-n): input characteristics are $I_B$ versus $V_{BE}$ at fixed $V_{CE}$; output characteristics are $I_C$ versus $V_{CE}$ at fixed $I_B$, showing a saturation region followed by a nearly flat active region. Current gain $\beta = \Delta I_{C}/\Delta I_{B}$ from the output curves.
Identifying components. A resistor has colour bands and conducts both ways; a capacitor blocks steady (dc) current but passes ac, storing energy in the electric field between two plates, while an inductor (typically a coil, sometimes wound on an iron core) opposes any change in current and offers negligible resistance to steady dc. Diodes and LEDs have a definite polarity marked on the body (a band near the cathode lead, or the shorter leg on an LED) and conduct in only one direction — connecting either backwards in a circuit gives no reading, or no light, rather than a reversed one.
Common Mistakes and Exam Traps
Misreading a vernier scale or picking the wrong coinciding division. Take the main-scale reading against the vernier's zero mark, then find the one vernier division that lines up most closely with any main-scale line — picking an adjacent division by mistake shifts the answer by exactly one least count, a very common source of an 'almost right' wrong answer.
Applying the zero-error correction with the wrong sign. The rule is always correct reading = observed reading − zero error; a positive zero error is subtracted, and subtracting a negative zero error effectively adds it back. Adding the zero error's magnitude regardless of its sign flips the answer in the wrong direction.
Ignoring which quantity dominates the percentage error. In $Z = A^pB^q/C^r$, the term with the largest power, not necessarily the one measured least precisely in absolute terms, usually dominates $\Delta Z/Z$ — this is why a radius (squared or cubed in most formulas) is generally the quantity worth measuring most carefully, even if some other length is read with a coarser instrument.
Timing too few oscillations in the pendulum experiment. Timing a single swing carries the observer's reaction-time error directly into T; timing 20–50 oscillations and dividing shrinks the fractional error proportionally, and since $g \propto 1/T^2$, any remaining error in T is doubled in the final error of g — skipping this step is a common reason for a poor experimental value of g.