Errors in measurement and combination of errors — practice questions

Question 1 · difficulty L2 · understanding

A physical quantity C is related to four other quantities $\mathrm{p}, \mathrm{q}, \mathrm{r}$ and s as follows $$C=\frac{p q^2}{r^3 \sqrt{s}}$$ The percentage errors in the measurement of $\mathrm{p}, \mathrm{q}, \mathrm{r}$ and s are $1 \%, 2 \%, 3 \%$ and $2 \%$, respectively. The percentage error in the measurement of $C$ will be__________%

Question 2 · difficulty L2 · understanding

A student in the laboratory measures thickness of a wire using screw gauge. The readings are 1.22 mm, 1.23 mm, 1.19 mm and 1.20 mm. The percentage error is $${x \over {121}}\%$$. The value of x is ____________.

Question 3 · difficulty L2 · understanding

For $$z = {a^2}{x^3}{y^{{1 \over 2}}}$$, where 'a' is a constant. If percentage error in measurement of 'x' and 'y' are 4% and 12% respectively, then the percentage error for 'z' will be _______________%.

Question 4 · difficulty L2 · understanding

The radius of a sphere is measured to be (7.50 $$\pm$$ 0.85) cm. Suppose the percentage error in its volume is x. The value of x, to the nearest x, is __________.

Question 5 · difficulty L2 · understanding

The resistance R = $${V \over I}$$, where V = (50 $$\pm$$ 2)V and I = (20 $$\pm$$ 0.2)A. The percentage error in R is 'x'%. The value of 'x' to the nearest integer is _________.

Question 6 · difficulty L2 · understanding

The dimensions of a cone are measured using a scale with a least count of $2 \mathrm{~mm}$. The diameter of the base and the height are both measured to be $20.0 \mathrm{~cm}$. The maximum percentage error in the determination of the volume is _______.

Question 7 · difficulty L2 · understanding

The percentage error in the calculated volume of a sphere, if there is $2 \%$ error in its diameter measurement, is $\_\_\_\_$ .

• A. 1
• B. 2
• C. 6
• D. 8

Question 8 · difficulty L2 · understanding

Four persons measure the length of a rod as $20.00 \mathrm{~cm}, 19.75 \mathrm{~cm}, 17.01 \mathrm{~cm}$ and 18.25 cm . The relative error in the measurement of average length of the rod is :

• A. 0.18
• B. 0.24
• C. 0.06
• D. 0.08

Question 9 · difficulty L2 · understanding

Keeping the significant figures in view, the sum of the physical quantities 52.01 m, 153.2 m and 0.123 m is :

• A. 205.3 m
• B. 205 m
• C. 205.333 m
• D. 205.33 m

Question 10 · difficulty L2 · understanding

In an experiment the values of two spring constants were measured as $k_1=(10 \pm 0.2) \mathrm{N} / \mathrm{m}$ and $k_2=(20 \pm 0.3) \mathrm{N} / \mathrm{m}$. If these springs are connected in parallel, then the percentage error in equivalent spring constant is :

• A. 1.33%
• B. $2.67 \%$
• C. 1.67%
• D. $2.33 \%$