Practical Physics flash cards

1. 1.What is the least count of a measuring instrument?

   The smallest measurement (change) that can be read reliably on the instrument. For a vernier: LC $=$ 1 main scale division $-$ 1 vernier scale division. For a screw gauge: LC $=$ pitch $/$ number of divisions on circular scale.

   Hint: Smallest reliably measurable change.

2. 2.Define the principle of a vernier scale.

   $n$ vernier scale divisions (VSD) are made equal in length to $(n-1)$ main scale divisions (MSD). This makes 1 VSD slightly smaller than 1 MSD, and the difference (1 MSD $-$ 1 VSD) is the least count.

   Hint: n VSD = (n−1) MSD.

3. 3.Give the formula for the least count of a vernier calliper.

   $\text{LC} = 1\text{ MSD} - 1\text{ VSD} = \dfrac{1\text{ MSD}}{n}$, where $n$ is the number of vernier divisions. Typical value: $1\text{ mm}/10 = 0.1\text{ mm} = 0.01\text{ cm}$.

   Hint: 1 MSD divided by number of VSD.

4. 4.How do you compute a vernier calliper reading?

   Reading $=$ main scale reading (MSR) $+$ (vernier coincidence $\times$ LC) $-$ zero error. The vernier coincidence is the VSD that best lines up with a main scale line.

   Hint: MSR + VC×LC − zero error.

5. 5.What is zero error in a vernier calliper and its two types?

   Zero error is the reading shown when the jaws are fully closed but the scale does not read zero. Positive: zero of vernier is to the right of main-scale zero (reading too high). Negative: zero of vernier is to the left (reading too low).

   Hint: Reading when jaws touch but scale ≠ 0.

6. 6.How is a positive zero error corrected in a vernier calliper?

   Positive zero error $=$ (coinciding VSD) $\times$ LC. It is subtracted from every observed reading: true reading $=$ observed $-$ (positive zero error).

   Hint: Subtract it; VC×LC.

7. 7.How is a negative zero error found and corrected in a vernier calliper?

   With jaws closed, note the vernier division $x$ that coincides; negative zero error $= -(n-x)\times \text{LC}$. Since it is negative, subtracting it means you add its magnitude to the observed reading.

   Hint: −(n−x)×LC; effectively add magnitude.

8. 8.Define pitch of a screw gauge / micrometer.

   Pitch is the linear distance the spindle advances along its axis in one complete rotation of the circular (thimble) scale. Commonly pitch $=$ distance moved in $k$ rotations divided by $k$; typical pitch $=1\text{ mm}$.

   Hint: Axial distance per one full turn.

9. 9.Give the formula for the least count of a screw gauge.

   $\text{LC} = \dfrac{\text{pitch}}{\text{number of divisions on circular scale}}$. For pitch $1\text{ mm}$ and $100$ divisions, $\text{LC} = 0.01\text{ mm} = 0.001\text{ cm} = 10\,\mu\text{m}$.

   Hint: Pitch ÷ circular divisions.

10. 10.How do you compute a screw gauge reading?

    Reading $=$ linear (pitch/main) scale reading $+$ (circular scale division $\times$ LC), then apply the zero-error correction.

    Hint: LSR + CSD×LC − zero error.

11. 11.Explain zero error in a screw gauge (positive and negative).

    With the faces just touching, if the circular-scale zero lies below the reference line, the error is positive (e.g. 3rd division $\Rightarrow +3\times\text{LC}$, subtract it). If the zero lies above the line, the error is negative (e.g. reads 97 $\Rightarrow -(100-97)\times\text{LC}$, add its magnitude).

    Hint: Below line = +, above line = −.

12. 12.What is a backlash error in a screw gauge and how is it avoided?

    Backlash error arises from loose/worn screw threads: on reversing rotation the spindle doesn't move immediately though the scale turns. Avoid it by always rotating the screw in the same direction while taking readings.

    Hint: Loose threads on reversal; turn one way only.

13. 13.What is the purpose of the ratchet on a screw gauge?

    The ratchet applies a fixed, limited pressure so the object is gripped consistently without over-tightening. It prevents excessive force that would compress the object or damage the threads, giving reproducible readings.

    Hint: Uniform pressure; prevents over-tightening.

14. 14.Define the least count of a spherometer.

    $\text{LC} = \dfrac{\text{pitch}}{\text{number of divisions on the circular disc}}$, exactly as for a screw gauge (a spherometer is essentially a fine screw with three fixed legs).

    Hint: Pitch ÷ disc divisions (like screw gauge).

15. 15.What does a spherometer measure and via which quantities?

    It measures the radius of curvature $R$ of a spherical surface (and thickness of thin plates). One measures the sagitta (height) $h$ at the centre and the mean distance $l$ between the outer legs.

    Hint: R of curved surface using h and leg spacing l.

16. 16.Give the radius of curvature formula used with a spherometer.

    $R = \dfrac{l^{2}}{6h} + \dfrac{h}{2}$, where $l$ is the mean distance between the three legs and $h$ is the sagitta. For small $h$, $R \approx \dfrac{l^{2}}{6h}$.

    Hint: R = l²/6h + h/2.

17. 17.In the meter bridge, what is measured and what is the balance condition?

    An unknown resistance $X$ is measured by balancing a Wheatstone bridge. At the null point (galvanometer shows zero), $\dfrac{X}{R} = \dfrac{l}{100-l}$, giving $X = R\,\dfrac{l}{100-l}$ with $l$ in cm.

    Hint: X = R·l/(100−l) at null.

18. 18.Why is the balance point kept near the middle of a meter bridge wire?

    Near the centre the fractional error in $X$ is minimized. The percentage error in $X$ is smallest when $l \approx 50\text{ cm}$; also end resistances and contact-resistance effects are relatively less significant there.

    Hint: Minimizes % error; l≈50 cm.

19. 19.What are end corrections in a meter bridge?

    Extra effective lengths at the two ends of the wire due to soldering, contact resistances and the finite width of copper strips. They are added to the measured lengths ($l+\alpha$ and $100-l+\beta$) and are found using a known resistance.

    Hint: Effective added lengths from contacts/solder.

20. 20.State Ohm's law and its experimental verification.

    $V = IR$: at constant temperature the current $I$ through a conductor is proportional to the potential difference $V$ across it. Verified by plotting $V$ vs $I$; a straight line through the origin confirms it, and its slope gives $R$.

    Hint: V∝I; V–I graph is a straight line, slope = R.

21. 21.How is resistivity $\rho$ of a wire found experimentally?

    Measure resistance $R$ (e.g. by meter bridge/Ohm's-law), length $L$, and radius $r$ (screw gauge). Then $\rho = \dfrac{R A}{L} = \dfrac{R\,\pi r^{2}}{L}$.

    Hint: ρ = Rπr²/L.

22. 22.In resistivity measurement, which quantity usually contributes the largest error and why?

    The wire radius $r$, because it is small and enters as $r^{2}$: $\dfrac{\Delta\rho}{\rho} = \dfrac{\Delta R}{R} + 2\dfrac{\Delta r}{r} + \dfrac{\Delta L}{L}$. Measure $r$ with a screw gauge at several places.

    Hint: r enters squared → doubled fractional error.

23. 23.What is the working principle of a potentiometer?

    For a uniform wire carrying a steady current, the potential drop is proportional to length: $V \propto l$, i.e. $V = kl$ where $k$ is the potential gradient (V per unit length). At balance no current flows through the galvanometer branch.

    Hint: V = k·l; potential gradient along uniform wire.

24. 24.Why is a potentiometer preferred over a voltmeter for measuring emf?

    At balance it draws no current from the cell, so it measures the true emf rather than terminal voltage (a voltmeter draws current and reads a slightly lower terminal p.d. due to internal resistance).

    Hint: Zero current at balance → true emf.

25. 25.How are two emfs compared with a potentiometer?

    Measure balancing lengths $l_1$ and $l_2$ for the two cells with the same potential gradient. Then $\dfrac{E_1}{E_2} = \dfrac{l_1}{l_2}$.

    Hint: E₁/E₂ = l₁/l₂.

26. 26.How is the internal resistance $r$ of a cell found with a potentiometer?

    Balance the cell's emf (open) at length $l_1$; then close a shunt resistance $R$ across it and balance the terminal p.d. at $l_2$. Then $r = R\left(\dfrac{l_1 - l_2}{l_2}\right)$.

    Hint: r = R(l₁−l₂)/l₂.

27. 27.What is the sensitivity of a potentiometer and how is it increased?

    Sensitivity means detecting small potential differences and giving large balancing lengths. It increases by decreasing the potential gradient $k$ — using a longer wire or reducing the driving current, so a small $V$ corresponds to a larger, more precisely read $l$.

    Hint: Lower potential gradient → higher sensitivity.

28. 28.Why must the driver cell emf exceed the emf being measured in a potentiometer?

    If the potential gradient over the whole wire is less than the cell's emf, no balance point exists on the wire (the galvanometer never nulls). The driver (auxiliary) emf must be larger than any emf being balanced.

    Hint: No null point otherwise.

29. 29.What does a sonometer investigate and what is the governing law?

    It studies vibrations of a stretched string. The fundamental frequency $f = \dfrac{1}{2L}\sqrt{\dfrac{T}{\mu}}$, where $L$ is the vibrating length, $T$ the tension, and $\mu$ the linear mass density.

    Hint: f = (1/2L)√(T/μ).

30. 30.State the three laws of a vibrating string (sonometer).

    (1) Law of length: $f \propto 1/L$ at fixed $T,\mu$. (2) Law of tension: $f \propto \sqrt{T}$ at fixed $L,\mu$. (3) Law of mass: $f \propto 1/\sqrt{\mu}$ at fixed $L,T$.

    Hint: f ∝ 1/L, ∝ √T, ∝ 1/√μ.

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