Errors in Measurement — MH-CET Physics MCQs with Solutions
Free MH-CET Physics Errors in Measurement MCQs with step-by-step solutions (21 questions). Part of Units and Measurements (Std 11). Practise online on Prepizo — no login needed.
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Questions with solutions
Q1 — Errors in Measurement · medium · theory
A systematic error is one that:
A. Is caused only by the observer
B. Tends to occur in one direction and can in principle be corrected ✓ Correct
C. Varies randomly in sign and magnitude
D. Cannot be reduced by any means
Solution: Zero errors and faulty calibration are typical examples.
Q2 — Errors in Measurement · medium · theory
A random error is one that:
A. Arises only from instrument design
B. Always shifts the result in one direction
C. Varies unpredictably in both sign and magnitude ✓ Correct
D. Can never be reduced
Solution: Averaging a large number of readings reduces it, unlike a systematic error.
Q3 — Errors in Measurement · easy · theory
The absolute error in a measurement is defined as:
A. The magnitude of the difference between the measured value and the true value ✓ Correct
B. The error expressed as a percentage
C. The smallest division of the instrument
D. The ratio of the error to the measured value
Solution: It carries the same unit as the quantity being measured.
Q4 — Errors in Measurement · easy · theory
The relative error in a measurement is defined as:
A. The mean absolute error divided by the mean value ✓ Correct
B. The least count of the instrument
C. The mean absolute error itself
D. The absolute error multiplied by $100$
Solution: Being a ratio, it is dimensionless; multiplying by $100$ gives the percentage error.
Q5 — Errors in Measurement · medium · theory
Instrumental errors, such as a zero error in a screw gauge, are classified as:
A. Random errors
B. Least count errors
C. Gross errors
D. Systematic errors ✓ Correct
Solution: They shift every reading in the same direction and can be removed by applying a correction.
Q6 — Errors in Measurement · easy · theory
Random errors in an experiment can be reduced by:
A. Taking a large number of readings and averaging them ✓ Correct
B. Changing the instrument each time
C. Using a single very careful reading
D. Ignoring the readings that differ most
Solution: Positive and negative fluctuations tend to cancel as the number of readings grows.
Q7 — Errors in Measurement · easy · theory
The least count of an instrument is:
A. The largest value it can measure
B. The smallest value it can measure reliably ✓ Correct
C. The average of its readings
D. The zero error of the instrument
Solution: It sets a floor on the precision achievable with that instrument.
Q8 — Errors in Measurement · medium · theory
When two quantities are added, the absolute errors:
A. Multiply
B. Add ✓ Correct
C. Subtract
D. Cancel out
Solution: The worst case is that both errors act in the same direction, so their magnitudes add.
Q9 — Errors in Measurement · medium · theory
When two quantities are multiplied, the percentage errors:
A. Add ✓ Correct
B. Remain unchanged
C. Multiply
D. Subtract
Solution: Relative errors combine additively for products and quotients alike.
Q10 — Errors in Measurement · hard · numerical
The density of a sphere is found from its mass and diameter. If the percentage errors are $1.5\%$ in mass and $1\%$ in diameter, the maximum percentage error in density is:
A. $3.5\%$
B. $4.5\%$ ✓ Correct
C. $2.5\%$
D. $5.5\%$
Solution: $\rho \propto \dfrac{M}{d^3}$, so the error is $1.5 + 3(1) = 4.5\%$.
Q11 — Errors in Measurement · medium · numerical
The percentage errors in mass and volume are $1\%$ and $2\%$. The maximum percentage error in density is:
A. $3\%$ ✓ Correct
B. $0.5\%$
C. $1\%$
D. $2\%$
Solution: $\rho = \dfrac{M}{V}$, so the relative errors add: $1 + 2 = 3\%$.
Q12 — Errors in Measurement · hard · numerical
For a quantity $x = \dfrac{a^2b}{c}$, the maximum relative error is:
A. $2\dfrac{\Delta a}{a} + \dfrac{\Delta b}{b} - \dfrac{\Delta c}{c}$
B. $\dfrac{\Delta a}{a} + \dfrac{\Delta b}{b} + \dfrac{\Delta c}{c}$
C. $2\dfrac{\Delta a}{a} + \dfrac{\Delta b}{b} + \dfrac{\Delta c}{c}$ ✓ Correct
D. $\dfrac{2\Delta a}{a} \times \dfrac{\Delta b}{b}$
Solution: Each exponent multiplies the corresponding relative error, and all contributions are added for the maximum error.
Q13 — Errors in Measurement · hard · numerical
The acceleration due to gravity is found from $g = \dfrac{4\pi^2l}{T^2}$. If the errors are $2\%$ in $l$ and $1\%$ in $T$, the percentage error in $g$ is:
A. $5\%$
B. $3\%$
C. $4\%$ ✓ Correct
D. $2\%$
Solution: $\dfrac{\Delta g}{g} = \dfrac{\Delta l}{l} + 2\dfrac{\Delta T}{T} = 2 + 2 = 4\%$.
Q14 — Errors in Measurement · medium · numerical
The radius of a sphere is measured with a $2\%$ error. The percentage error in its volume is:
A. $6\%$ ✓ Correct
B. $8\%$
C. $2\%$
D. $4\%$
Solution: $V \propto r^3$, so the error is $3 \times 2 = 6\%$.
Q15 — Errors in Measurement · medium · numerical
The radius of a circle is measured with a $2\%$ error. The percentage error in its area is:
A. $1\%$
B. $2\%$
C. $6\%$
D. $4\%$ ✓ Correct
Solution: $A \propto r^2$, so the error is $2 \times 2 = 4\%$.
Q16 — Errors in Measurement · medium · numerical
The side of a cube is measured with a $1\%$ error. The percentage error in its volume is:
A. $1\%$
B. $3\%$ ✓ Correct
C. $6\%$
D. $2\%$
Solution: $V \propto a^3$, so the error is tripled.
Q17 — Errors in Measurement · medium · numerical
Four readings of a length are $10.2$, $10.4$, $10.6$ and $10.8\text{ cm}$. The mean value is:
A. $10.4\text{ cm}$
B. $41.0\text{ cm}$
C. $10.5\text{ cm}$ ✓ Correct
D. $10.6\text{ cm}$
Solution: Mean $= \dfrac{10.2 + 10.4 + 10.6 + 10.8}{4} = \dfrac{42.0}{4} = 10.5\text{ cm}$.
Q18 — Errors in Measurement · hard · numerical
For the readings $10.2$, $10.4$, $10.6$ and $10.8\text{ cm}$ with mean $10.5\text{ cm}$, the mean absolute error is:
A. $0.1\text{ cm}$
B. $0.3\text{ cm}$
C. $0.6\text{ cm}$
D. $0.2\text{ cm}$ ✓ Correct
Solution: The absolute errors are $0.3$, $0.1$, $0.1$ and $0.3\text{ cm}$, whose mean is $\dfrac{0.8}{4} = 0.2\text{ cm}$.
Q19 — Errors in Measurement · medium · numerical
A length of $10\text{ cm}$ is measured with an absolute error of $0.05\text{ cm}$. The percentage error is:
A. $0.5\%$ ✓ Correct
B. $5\%$
C. $2\%$
D. $0.05\%$
Solution: $\dfrac{0.05}{10} \times 100 = 0.5\%$.
Q20 — Errors in Measurement · hard · numerical
Two lengths $5.0 \pm 0.1\text{ cm}$ and $3.0 \pm 0.2\text{ cm}$ are added. The result is:
A. $8.0 \pm 0.1\text{ cm}$
B. $8.0 \pm 0.3\text{ cm}$ ✓ Correct
C. $2.0 \pm 0.3\text{ cm}$
D. $8.0 \pm 0.15\text{ cm}$
Solution: For a sum the absolute errors add: $0.1 + 0.2 = 0.3\text{ cm}$.
Q21 — Errors in Measurement · easy · numerical
A quantity is measured as $2.00\text{ m}$ with a relative error of $0.01$. The percentage error is:
A. $0.01\%$
B. $1\%$ ✓ Correct
C. $0.1\%$
D. $10\%$
Solution: Percentage error is the relative error multiplied by $100$.