Questions & explanations
1. In an experiment to determine the Young's modulus of a wire by Searle's method, which of the following is a systematic error that can be minimised by proper zero adjustment of the measuring instrument?
- Parallax error while reading the extension scale
- Random error due to temperature fluctuations
- Zero error in the micrometer screw gauge used to measure wire diameter
- Error due to variation in the applied load
Answer: Zero error in the micrometer screw gauge used to measure wire diameter
Zero error is a systematic error that shifts all readings by a constant amount. It can be minimised by noting and compensating for the zero reading of the instrument before taking measurements. Parallax error is a personal error that can be avoided by taking readings with the eye perpendicular to the scale. Random errors like temperature fluctuations and load variation are not fixed and cannot be corrected by zero adjustment; they are minimised by averaging multiple readings.
2. In an experiment to verify Ohm's law, a student plots a graph of voltage (V) on the y-axis against current (I) on the x-axis for a metallic conductor. The resulting graph is a straight line passing through the origin. The slope of this graph represents:
- Conductance of the conductor
- Resistance of the conductor
- Resistivity of the conductor
- Power dissipated in the conductor
Answer: Resistance of the conductor
For an ohmic conductor, V = IR, so when V is plotted on the y-axis and I on the x-axis, the slope is V/I = R, which is the resistance. Conductance is the reciprocal (I/V) and would be the slope if the axes were swapped. Resistivity is a material property related to resistance through geometry, and power is V × I, not directly obtained from the slope.
3. In a vernier callipers, N divisions of the vernier scale coincide with (N-1) divisions of the main scale. If one main scale division is 1 mm, the least count of the instrument is:
- 1/N mm
- 1/(N-1) mm
- N mm
- (N-1)/N mm
Answer: 1/N mm
The least count is the ratio of the value of one main scale division to the total number of vernier divisions. Given 1 M.S.D. = 1 mm and N V.S.D. = (N-1) M.S.D., so 1 V.S.D. = (N-1)/N mm. Least count = 1 M.S.D. - 1 V.S.D. = 1 - (N-1)/N = 1/N mm.
4. In a metre bridge experiment, a known resistance of 10 Ω is placed in the left gap and an unknown resistance R in the right gap. The null point is obtained at 40 cm from the left end. The value of R is:
- 15 Ω
- 6.67 Ω
- 10 Ω
- 20 Ω
Answer: 15 Ω
In a metre bridge the balance condition is P/R = l₁/(100 − l₁), where P is the resistance in the left gap and l₁ is the balance length from the left end. Here P = 10 Ω and l₁ = 40 cm, so 10/R = 40/60, giving R = 10 × 60/40 = 15 Ω.
5. In an experiment to find the focal length of a convex lens by the u-v method, the object distance u is 20 cm and the image distance v is 30 cm. The focal length f of the lens is:
- 12 cm
- 10 cm
- 15 cm
- 20 cm
Answer: 12 cm
Using the lens formula State using NCERT sign convention: u = −20 cm, v = +30 cm, so 1/f = 1/v − 1/u = 1/30 − (1/−20) = 1/30 + 1/20 = 1/12, f = 12 cm. = (2+3)/60 = 5/60 → f = 12 cm.
6. A metre scale has a zero error of +0.3 cm. The measured length of an object using this scale is 5.2 cm. What is the correct length?
- 5.5 cm
- 4.9 cm
- 5.2 cm
- 5.0 cm
Answer: 4.9 cm
A positive zero error means the scale reads more than the actual length. Hence the correct length = measured length - zero error = 5.2 cm - 0.3 cm = 4.9 cm.
7. The figure of merit of a galvanometer is defined as:
- the current required to produce a deflection of one division
- the voltage required to produce a deflection of one division
- the resistance of the galvanometer
- the sensitivity of the galvanometer
Answer: the current required to produce a deflection of one division
Figure of merit is defined as the current (in amperes) that causes a deflection of one division on the scale. It is the reciprocal of current sensitivity.