Error of Measurement

Q 1 :

In an experiment to measure focal length $(f)$ of convex lens, the least count of the measuring scales for the position of object ( $u$ ) and for the position of image ( $v$ ) are $∆ u$ and $∆ v,$ respectively. The error in the measurement of the focal length of the convex lens will be [2024]

$2 f [\frac{∆ u}{u} + \frac{∆ v}{v}]$
$f [\frac{∆ u}{u} + \frac{∆ v}{v}]$
$\frac{∆ u}{u} + \frac{∆ v}{v}$
$f^{2} [\frac{∆ u}{u^{2}} + \frac{∆ v}{v^{2}}]$

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(4)

$\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$

$\frac{- 1}{v^{2}} d v + \frac{1}{u^{2}} d u = \frac{- 1}{f^{2}} d f \Rightarrow \frac{d f}{f^{2}} = \frac{d v}{v^{2}} + \frac{d u}{u^{2}}$

$d f = f^{2} [\frac{d v}{v^{2}} + \frac{d u}{u^{2}}] \Rightarrow ∆ f = f^{2} (\frac{∆ v}{v^{2}} + \frac{∆ u}{u^{2}})$

Q 2 :

To find the spring constant ( $k$ ) of a spring experimentally, a student commits 2% positive error in the measurement of time and 1% negative error in measurement of mass. The percentage error in determining value of $k$ is: [2024]

3%
4%
5%
1%

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(1)

$T = 2 π \sqrt{\frac{m}{k}} \Rightarrow k = 4 π^{2} \cdot \frac{m}{T^{2}}$

$\frac{∆ k}{k} = \frac{∆ m}{m} + 2 \cdot \frac{∆ T}{T} \Rightarrow \frac{∆ k}{k} % = \frac{∆ m}{m} % + \frac{2 ∆ T}{T} %$

(We always take maximum error)

$\frac{∆ k}{k} % = (- 1) % + 2 (2) % = | - 3 % | = 3 %$

Q 3 :

Young's modulus is determined by the equation given by $Y = 49000 \frac{m}{L} \frac{d y n e}{c m^{2}}$ where M is the mass and L is the extension of wire used in the experiment. Now error in Young's modules ( $Y$ ) is estimated by taking data from $M - L$ plot in graph paper. The smallest scale divisions are 5g and 0.02 cm along load axis and extension axis respectively. If the value of $M$ and are 500 g and 2 cm respectively then percentage error of $Y$ is [2024]

0.2%
0.02%
2%
0.5%

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(3)

$\frac{∆ Y}{Y} = \frac{∆ m}{m} + \frac{∆ l}{l}$

$= \frac{5}{500} + \frac{0.02}{2} = 0.01 + 0.01 \frac{∆ Y}{Y}$

$% \frac{∆ Y}{Y} = 2 %$

Q 4 :

The resistance $R = V / I$ where $V = (200 \pm 5) V$ and $I = (20 \pm 0.2) A .$ The percentage error in the measurement of R is: [2024]

3.5%
7%
3%
5.5%

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(1)

We have, $R = V / I$

According to error analysis, maximum fractional error.

$\frac{d R}{R} = \frac{d V}{V} + \frac{d I}{I}$

$\frac{d R}{R} = \frac{5}{200} + \frac{0.2}{20} = \frac{7}{200}$

Hence, % error $\frac{d R}{R} \times 100 = \frac{7}{200} \times 100 = 3.5 %$

Q 5 :

A physical quantity $Q$ is found to depend on quantities $a, b, c$ by the relation $Q = \frac{a^{4} b^{3}}{c^{2}} .$ The percentage error in $a, b$ and $c$ are 3%, 4% and 5% respectively. Then, the percentage error in $Q$ is [2024]

66%
14%
34%
43%

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(3)

$\frac{∆ Q}{Q} = 4 \frac{∆ a}{a} + 3 \frac{∆ b}{b} + 2 \frac{∆ c}{c}$

$Q = 4 \times 3 % + 3 \times 4 % + 2 \times 5 %$

$= 12 % + 12 % + 10 % = 34 %$

Q 6 :

If the percentage errors in measuring the length and the diameter of a wire are 0.1% each. The percentage error in measuring its resistance will be [2024]

0.2%
0.144%
0.3%
0.1%

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(3)

$R = \frac{ρ L}{π \frac{d^{2}}{4}}$

$\frac{∆ R}{R} = \frac{∆ L}{L} + \frac{2 ∆ d}{d}$

$\frac{∆ L}{L} = 0.1 %$ and $\frac{∆ d}{d} = 0.1 %$

$\frac{∆ R}{R} = 0.3 %$

Q 7 :

The measured value of the length of a simple pendulum is 20 cm with 2 mm accuracy. The time for 50 oscillations was measured to be 40 seconds with 1 second resolution. From these measurements, the accuracy in the measurement of acceleration due to gravity is N%. The value of N is: [2024]

4
8
6
5

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(3)

$T = 2 π \sqrt{\frac{l}{g}}$

$g = \frac{4 π^{2} l}{T^{2}}$

$\frac{∆ g}{g} = \frac{∆ l}{l} + \frac{2 ∆ T}{T} = \frac{0.2}{20} + 2 (\frac{1}{40}) = \frac{1.2}{20}$

Percentage change = $\frac{1.2}{20} \times 100 = 6 %$

Q 8 :

The radius ( $r$ ), length ( $l$ ) and resistance ( $R$ ) of a metal wire was measured in the laboratory as [2024]

$r = (0.35 \pm 0.05) c m$

$R = (100 \pm 10) o h m$

$l = (15 \pm 0.2) c m$

The percentage error in resistivity of the material of the wire is

25.6%
39.9%
37.3%
35.6%

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(2)

$\frac{∆ ρ}{ρ} = \frac{∆ R}{R} + 2 \frac{∆ r}{r} + \frac{∆ l}{l}$

$= \frac{10}{100} + 2 \times \frac{0.05}{0.35} + \frac{0.2}{15}$

$= \frac{1}{10} + \frac{2}{7} + \frac{1}{75}$

$\frac{∆ ρ}{ρ} = 39.9 %$

Q 9 :

The maximum percentage error in the measurement of density of a wire is

[Given, mass of wire = (0.60 $\pm$ 0.003) g

radius of wire = (0.50 $\pm$ 0.01) cm

length of wire = (10.00 $\pm$ 0.05) cm] [2025]

4
5
8
7

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(2)

$ρ = \frac{m}{v o l .} = \frac{m}{π R^{2} l} \Rightarrow \frac{d ρ}{ρ} = \frac{d m}{m} + \frac{2 d R}{R} + \frac{d l}{l}$

$∴ \frac{d ρ}{ρ} = (\frac{0.003}{0.6} + \frac{2 \times 0.01}{0.5} + \frac{0.05}{10}) 100 = 5 %$

Q 10 :

The energy of a system is given as $E (t) = α^{3} e^{- β t}$ , where t is the time and $β = 0.3 s^{- 1}$ . The error in the measurement of $α$ and t are 1.2% and 1.6%, respectively. At t = 5 s, maximum percentage error in the energy is [2025]

4%
11.6%
6%
8.4%

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(3)

$d E = 3 α^{2} d α e^{- β t} + α^{3} e^{- β t} (- β) d t$

$\frac{d E}{E} = \frac{3 d α}{α} + (- β) d t$

$\frac{△ E}{E} = \frac{3 △ α}{α} + β △ t$

$(%) △ T = 1.6 \times 5 = 8 %$

$% (\frac{3 △ α}{α}) = 3 \times 1.2 % = 3.6 %$

Putting values we get,

$\frac{△ E}{E} % = 3.6 + 8 \times 0.3 = 6 %$ .

Q 11 :

A quantity Q is formulated as $X^{- 2} Y^{+ \frac{3}{2}} Z^{- \frac{2}{5}} \cdot X, Y$ , and Z are independent parameters which have fractional errors of 0.1, 0.2 and 0.5, respectively in measurement. The maximum fractional error of Q is [2025]

0.1
0.8
0.7
0.6

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(3)

Fractional error $= 2 \frac{△ X}{X} + \frac{3}{2} \frac{△ Y}{Y} + \frac{2}{5} \frac{△ Z}{Z}$

$= 2 (0.1) + \frac{3}{2} (0.2) + \frac{2}{5} (0.5)$

= 0.2 + 0.3 + 0.2 = 0.7

Q 12 :

A physical quantity Q is related to four observables a, b, c, d as follows:

$Q = \frac{a b^{4}}{c d} where, a = (60 \pm 3) P a; b = (20 \pm 0.1) m$ ,

$c = (40 \pm 0.2) {Nsm}^{- 2} and d = (50 \pm 0.1) m$ ,

then the percentage error in Q is $\frac{x}{1000}$ , where x = __________. [2025]

(77)

$Q = \frac{a b^{4}}{c d}$

$\Rightarrow \frac{△ Q}{Q} = [\frac{△ a}{a} + 4 \frac{△ b}{b} + \frac{△ c}{c} + \frac{△ d}{d}]$

$\Rightarrow \frac{x}{1000} = [\frac{3}{60} + 4 (\frac{0.1}{20}) + (\frac{0.2}{40}) + \frac{0.1}{50}]$

$\Rightarrow x = 77$

Q 13 :

A physical quantity C is related to four other quantities p, q, r and s as follows

$C = \frac{p q^{2}}{r^{3} \sqrt{s}}$

The percentage errors in the measurement of p, q, r and s are 1%, 2%, 3% and 2% respectively. The percentage error in the measurement of C will be __________ %. [2025]

(15)

$C = p^{1} q^{2} r^{- 3} s^{- 1 / 2}$

${(\frac{d C}{C})}_{\max} = \frac{d P}{P} + \frac{2 d q}{q} + \frac{3 d r}{r} + \frac{1}{2} \frac{d s}{s}$

$= (1 + 2 \times 2 + 3 \times 3 + \frac{1}{2} \times 2) % = 15 %$

Q 14 :

Two resistances are given as $R_{1} = (10 \pm 0.5) Ω$ and $R_{2} = (15 \pm 0.5) Ω$ . The percentage error in the measurement of equivalent resistance when they are connected in parallel is [2023]

6.33
5.33
2.33
4.33

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(4)

$\frac{1}{R} = \frac{1}{R_{1}} + \frac{1}{R_{2}}$

Differentiating both sides, we get

$\frac{△ R}{R^{2}} = \frac{△ R_{1}}{R_{1}^{2}} + \frac{△ R_{2}}{R_{2}^{2}} [R = \frac{R_{1} R_{2}}{R_{1} + R_{2}} = \frac{10 \times 15}{10 + 15} = 6]$

$\Rightarrow \frac{△ R}{R} = (\frac{△ R_{1}}{R_{1}^{2}} + \frac{△ R_{2}}{R_{2}^{2}}) R$

$\Rightarrow (\frac{0.5}{100} + \frac{0.5}{225}) 6 = (\frac{6 \times 0.5}{25}) (\frac{1}{4} + \frac{1}{9}) = \frac{13}{100}$

$\frac{△ R}{R} \times 100 = \frac{13}{3} = 4.33 %$

Q 15 :

A 2 meter long scale with least count of 0.2 cm is used to measure the locations of objects on an optical bench. While measuring the focal length of a convex lens, the object pin and the convex lens are placed at 80 cm mark and 1 m mark, respectively. The image of the object pin on the other side of lens coincides with image pin that is kept at 180 cm mark. The % error in the estimation of focal length is [2023]

1.02
0.85
1.70
0.51

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(3)

Least count of the scale is 0.2 cm

u = (100 $\pm$ 0.2) – (80 $\pm$ 0.2) = (20 $\pm$ 0.4) cm

v = (180 $\pm$ 0.2) – (100 $\pm$ 0.2) = (80 $\pm$ 0.4) cm

From lens formula,

$\frac{1}{v} - \frac{1}{u} = \frac{1}{f} \Rightarrow \frac{1}{f} = \frac{1}{80} - \frac{1}{- 20} \Rightarrow f = 16 cm$

Also, $\frac{△ v}{v^{2}} + \frac{△ u}{u^{2}} = \frac{△ f}{f^{2}}$

$\Rightarrow \frac{△ f}{f} \times 100 = (\frac{△ v}{v^{2}} + \frac{△ u}{u^{2}}) \times f \times 100$

$\Rightarrow % f = (\frac{0.4}{400} + \frac{0.4}{6400}) \times 16 \times 100 = 1.70$

Q 16 :

A cylindrical wire of mass (0.4 $\pm$ 0.01) g has length (8 $\pm$ 0.04) cm and radius (6 $\pm$ 0.03) cm. The maximum error in its density will be [2023]

1%
4%
5%
3.5%

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(2)

$ρ = \frac{m}{π r^{2} l} \Rightarrow$ $| \frac{d ρ}{ρ} |_{\max}$ $=$ $| \frac{d m}{m} |$ $+ 2$ $| \frac{d r}{r} |$ $+$ $| \frac{d l}{l} |$

$= \frac{0.01}{0.4} + \frac{2 (0.03)}{6} + \frac{0.04}{8}$

$\Rightarrow % error in density = (\frac{d ρ}{ρ}) \times 100 %$

$= (2.5 + 1 + 0.5) % = 4 %$

Q 17 :

A physical quantity P is given as $P = \frac{a^{2} b^{3}}{c \sqrt{d}}$ . The percentage error in the measurement of a, b, c and d are 1%, 2%, 3% and 4% respectively. The percentage error in the measurement of quantity P will be [2023]

13%
14%
12%
16%

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(1)

$\frac{△ P}{P} \times 100 % = (2 \frac{△ a}{a} + 3 \frac{△ b}{b} + \frac{△ c}{c} + \frac{1}{2} \frac{△ d}{d}) \times 100 %$

$= 2 (1 %) + 3 (2 %) + 3 % + \frac{1}{2} \times 4 % = 13 %$

Q 18 :

A body of mass (5 $\pm$ 0.5) kg is moving with a velocity of (20 $\pm$ 0.4) m/s. Its kinetic energy will be [2023]

(1000 $\pm$ 140) J
(1000 $\pm$ 0.14) J
(500 $\pm$ 0.14) J
(500 $\pm$ 140) J

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(1)

$k = \frac{1}{2} m v^{2}$

$k = \frac{1}{2} \times 5 \times 400 = 5 \times 200 = 1000 J$

$\frac{△ k}{k} = \frac{△ m}{m} + \frac{2 △ v}{v} = \frac{0.5}{5} + \frac{2 \times 0.4}{20}$

$△ k = 1000 (\frac{1}{10} + \frac{4}{100}) = 1000 (\frac{10 + 4}{100}) = 140 J$

Q 19 :

Four persons measure the length of a rod as 20.00 cm, 19.75 cm, 17.01 cm, and 18.25 cm. The relative error in the measurement of average length of the rod is: [2026]

0.08
0.18
0.24
0.06

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(4)

$ℓ_{mean} = \frac{ℓ_{1} + ℓ_{2} + ℓ_{3} + ℓ_{4}}{4}$

$ℓ_{mean} = \frac{20.00 + 19.75 + 17.01 + 18.25}{4}$

$= 18.75$

$Δ ℓ_{mean} = \frac{| Δ ℓ_{1} | + | Δ ℓ_{2} | + | Δ ℓ_{3} | + | Δ ℓ_{4} |}{4}$

$= \frac{1.25 + 1 + 1.74 + 0.5}{4} = 1.12$

$So, relative error$

$= \frac{Δ ℓ_{mean}}{ℓ_{mean}}$ $= \frac{1.12}{18.75}$ $= 0.06$

Q 20 :

In an experiment the values of two spring constants were measured as $k_{1} = (10 \pm 0.2) N/m$ and $k_{2} = (20 \pm 0.3) N/m$ . If these springs are connected in parallel, then the percentage error in the equivalent spring constant is: [2026]

1.67%
2.67%
2.33%
1.33%

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(1)

For parallel combination of spring,

$K_{eq} = K_{1} + K_{2} = 30 N/m$

$Δ K_{eq} = Δ K_{1} + Δ K_{2} = 0.2 + 0.3 = 0.5 N/m$

$∴$ $% Error in K = \frac{0.5}{30} \times 100 = 1.67 %$

Q 21 :

The time period of a simple harmonic oscillator is $T = 2 π \sqrt{\frac{k}{m}} .$ Measured value of mass (m) of the object is 10 g with an accuracy of 10 mg and time for 50 oscillations of the spring is found to be 60 s using a watch of 2 s resolution. Percentage error in determination of spring constant (k) is ______ %. [2026]

3.35
6.76
7.60
3.43

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(2)

$\frac{Δ K}{K} = \frac{2 Δ T}{T} + \frac{Δ m}{m}$

$T = \frac{60}{50} = 1.2 sec$

$Δ T = \frac{2}{50}$

$∴$ $\frac{Δ K}{K} = \frac{2 \times 2}{50 \times 1.2} + \frac{10 \times 10^{- 3}}{10} = 0.0676$

$∴$ $% Error = 6.76 %$

Q 22 :

A spherical body of radius r and density $σ$ falls freely through a viscous liquid having density $ρ$ and viscosity $η$ and attains a terminal velocity $v_{0}$ . Estimated maximum error in the quantity $η$ is: (Ignore errors associated with $σ, ρ a n d g,$ gravitational acceleration) [2026]

$2 [[\frac{Δ r}{r} - \frac{Δ v_{0}}{v_{0}}]]$
$2 [[\frac{Δ r}{r} + \frac{Δ v_{0}}{v_{0}}]]$
$2 \frac{Δ r}{r} - \frac{Δ v_{0}}{v_{0}}$
$\frac{2 Δ r}{r} + \frac{Δ v_{0}}{v_{0}}$

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(4)

$V_{0} = \frac{2 r^{2} g}{9 n} (ρ_{B} - ρ_{L})$

$n = \frac{2 r^{2} g}{9 V_{0}} (ρ_{B} - ρ_{L})$

$\frac{Δ n}{n} = \frac{2 Δ r}{r} + \frac{Δ V_{0}}{V_{0}}$

Q 23 :

If E and H represent the intensity of electric field and magnetising field respectively, then the unit of E/H will be

ohm
newton
mho
joule

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4

Select one or more options

If E and H represent the intensity of electric field and magnetising field respectively, then the unit of E/H will be

write answer: ohm, newton & mho

Topic Question Set

Q 2 :

To find the spring constant ( $k$ ) of a spring experimentally, a student commits 2% positive error in the measurement of time and 1% negative error in measurement of mass. The percentage error in determining value of $k$ is: [2024]

Q 4 :

The resistance $R = V / I$ where $V = (200 \pm 5) V$ and $I = (20 \pm 0.2) A .$ The percentage error in the measurement of R is: [2024]

Q 5 :

A physical quantity $Q$ is found to depend on quantities $a, b, c$ by the relation $Q = \frac{a^{4} b^{3}}{c^{2}} .$ The percentage error in $a, b$ and $c$ are 3%, 4% and 5% respectively. Then, the percentage error in $Q$ is [2024]

Q 6 :

If the percentage errors in measuring the length and the diameter of a wire are 0.1% each. The percentage error in measuring its resistance will be [2024]

Q 7 :

The measured value of the length of a simple pendulum is 20 cm with 2 mm accuracy. The time for 50 oscillations was measured to be 40 seconds with 1 second resolution. From these measurements, the accuracy in the measurement of acceleration due to gravity is N%. The value of N is: [2024]

Q 8 :

The radius ( $r$ ), length ( $l$ ) and resistance ( $R$ ) of a metal wire was measured in the laboratory as [2024]

$r = (0.35 \pm 0.05) c m$

$R = (100 \pm 10) o h m$

$l = (15 \pm 0.2) c m$

The percentage error in resistivity of the material of the wire is

Q 9 :

The maximum percentage error in the measurement of density of a wire is

[Given, mass of wire = (0.60 $\pm$ 0.003) g

radius of wire = (0.50 $\pm$ 0.01) cm

length of wire = (10.00 $\pm$ 0.05) cm] [2025]

Q 10 :

The energy of a system is given as $E (t) = α^{3} e^{- β t}$ , where t is the time and $β = 0.3 s^{- 1}$ . The error in the measurement of $α$ and t are 1.2% and 1.6%, respectively. At t = 5 s, maximum percentage error in the energy is [2025]

Q 11 :

A quantity Q is formulated as $X^{- 2} Y^{+ \frac{3}{2}} Z^{- \frac{2}{5}} \cdot X, Y$ , and Z are independent parameters which have fractional errors of 0.1, 0.2 and 0.5, respectively in measurement. The maximum fractional error of Q is [2025]

Q 12 :

A physical quantity Q is related to four observables a, b, c, d as follows:

$Q = \frac{a b^{4}}{c d} where, a = (60 \pm 3) P a; b = (20 \pm 0.1) m$ ,

$c = (40 \pm 0.2) {Nsm}^{- 2} and d = (50 \pm 0.1) m$ ,

then the percentage error in Q is $\frac{x}{1000}$ , where x = __________. [2025]

Q 13 :

A physical quantity C is related to four other quantities p, q, r and s as follows

$C = \frac{p q^{2}}{r^{3} \sqrt{s}}$

The percentage errors in the measurement of p, q, r and s are 1%, 2%, 3% and 2% respectively. The percentage error in the measurement of C will be __________ %. [2025]

Q 14 :

Two resistances are given as $R_{1} = (10 \pm 0.5) Ω$ and $R_{2} = (15 \pm 0.5) Ω$ . The percentage error in the measurement of equivalent resistance when they are connected in parallel is [2023]

Q 16 :

A cylindrical wire of mass (0.4 $\pm$ 0.01) g has length (8 $\pm$ 0.04) cm and radius (6 $\pm$ 0.03) cm. The maximum error in its density will be [2023]

Q 17 :

A physical quantity P is given as $P = \frac{a^{2} b^{3}}{c \sqrt{d}}$ . The percentage error in the measurement of a, b, c and d are 1%, 2%, 3% and 4% respectively. The percentage error in the measurement of quantity P will be [2023]

Q 18 :

A body of mass (5 $\pm$ 0.5) kg is moving with a velocity of (20 $\pm$ 0.4) m/s. Its kinetic energy will be [2023]

Q 19 :

Four persons measure the length of a rod as 20.00 cm, 19.75 cm, 17.01 cm, and 18.25 cm. The relative error in the measurement of average length of the rod is: [2026]

Q 20 :

In an experiment the values of two spring constants were measured as $k_{1} = (10 \pm 0.2) N/m$ and $k_{2} = (20 \pm 0.3) N/m$ . If these springs are connected in parallel, then the percentage error in the equivalent spring constant is: [2026]

Q 23 :

If E and H represent the intensity of electric field and magnetising field respectively, then the unit of E/H will be

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Topic Question Set

Q 1 : In an experiment to measure focal length (f) of convex lens, the least count of the measuring scales for the position of object (u) and for the position of image (v) are ∆u and ∆v, respectively. The error in the measurement of the focal length of the convex lens will be [2024]

Q 2 : To find the spring constant (k) of a spring experimentally, a student commits 2% positive error in the measurement of time and 1% negative error in measurement of mass. The percentage error in determining value of k is: [2024]

Q 4 : The resistance R=V/I where V=(200±5)V and I=(20±0.2)A. The percentage error in the measurement of R is: [2024]

Q 5 : A physical quantity Q is found to depend on quantities a,b,c by the relation Q=a4b3c2. The percentage error in a,b and c are 3%, 4% and 5% respectively. Then, the percentage error in Q is [2024]

Q 6 : If the percentage errors in measuring the length and the diameter of a wire are 0.1% each. The percentage error in measuring its resistance will be [2024]

Q 7 : The measured value of the length of a simple pendulum is 20 cm with 2 mm accuracy. The time for 50 oscillations was measured to be 40 seconds with 1 second resolution. From these measurements, the accuracy in the measurement of acceleration due to gravity is N%. The value of N is: [2024]

Q 8 : The radius (r), length (l) and resistance (R) of a metal wire was measured in the laboratory as [2024] r=(0.35±0.05)cm R=(100±10)ohm l=(15±0.2)cm The percentage error in resistivity of the material of the wire is

Q 9 : The maximum percentage error in the measurement of density of a wire is [Given, mass of wire = (0.60 ± 0.003) g radius of wire = (0.50 ± 0.01) cm length of wire = (10.00 ± 0.05) cm] [2025]

Q 10 : The energy of a system is given as E(t)=α3e–βt, where t is the time and β=0.3 s–1. The error in the measurement of α and t are 1.2% and 1.6%, respectively. At t = 5 s, maximum percentage error in the energy is [2025]

Q 11 : A quantity Q is formulated as X–2Y+32Z–25·X,Y, and Z are independent parameters which have fractional errors of 0.1, 0.2 and 0.5, respectively in measurement. The maximum fractional error of Q is [2025]

Q 12 : A physical quantity Q is related to four observables a, b, c, d as follows: Q=ab4cd where, a=(60±3) Pa; b=(20±0.1) m, c=(40±0.2) Nsm–2 and d=(50±0.1) m, then the percentage error in Q is x1000, where x = __________. [2025]

Q 13 : A physical quantity C is related to four other quantities p, q, r and s as follows C=pq2r3s The percentage errors in the measurement of p, q, r and s are 1%, 2%, 3% and 2% respectively. The percentage error in the measurement of C will be __________ %. [2025]

Q 14 : Two resistances are given as R1=(10±0.5)Ω and R2=(15±0.5)Ω. The percentage error in the measurement of equivalent resistance when they are connected in parallel is [2023]

Q 16 : A cylindrical wire of mass (0.4 ± 0.01) g has length (8 ± 0.04) cm and radius (6 ± 0.03) cm. The maximum error in its density will be [2023]

Q 17 : A physical quantity P is given as P=a2b3cd. The percentage error in the measurement of a, b, c and d are 1%, 2%, 3% and 4% respectively. The percentage error in the measurement of quantity P will be [2023]

Q 18 : A body of mass (5 ± 0.5) kg is moving with a velocity of (20 ± 0.4) m/s. Its kinetic energy will be [2023]

Q 19 : Four persons measure the length of a rod as 20.00 cm, 19.75 cm, 17.01 cm, and 18.25 cm. The relative error in the measurement of average length of the rod is: [2026]

Q 20 : In an experiment the values of two spring constants were measured as k1=(10±0.2) N/m and k2=(20±0.3) N/m. If these springs are connected in parallel, then the percentage error in the equivalent spring constant is: [2026]

Q 22 : A spherical body of radius r and density σ falls freely through a viscous liquid having density ρ and viscosity η and attains a terminal velocity v0. Estimated maximum error in the quantity η is: (Ignore errors associated with σ, ρ and g,gravitational acceleration) [2026]

Q 23 : If E and H represent the intensity of electric field and magnetising field respectively, then the unit of E/H will be

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Q 2 :

To find the spring constant ( $k$ ) of a spring experimentally, a student commits 2% positive error in the measurement of time and 1% negative error in measurement of mass. The percentage error in determining value of $k$ is: [2024]

Q 4 :

The resistance $R = V / I$ where $V = (200 \pm 5) V$ and $I = (20 \pm 0.2) A .$ The percentage error in the measurement of R is: [2024]

Q 5 :

A physical quantity $Q$ is found to depend on quantities $a, b, c$ by the relation $Q = \frac{a^{4} b^{3}}{c^{2}} .$ The percentage error in $a, b$ and $c$ are 3%, 4% and 5% respectively. Then, the percentage error in $Q$ is [2024]

Q 6 :

If the percentage errors in measuring the length and the diameter of a wire are 0.1% each. The percentage error in measuring its resistance will be [2024]

Q 7 :

The measured value of the length of a simple pendulum is 20 cm with 2 mm accuracy. The time for 50 oscillations was measured to be 40 seconds with 1 second resolution. From these measurements, the accuracy in the measurement of acceleration due to gravity is N%. The value of N is: [2024]

Q 8 :

The radius ( $r$ ), length ( $l$ ) and resistance ( $R$ ) of a metal wire was measured in the laboratory as [2024]

$r = (0.35 \pm 0.05) c m$

$R = (100 \pm 10) o h m$

$l = (15 \pm 0.2) c m$

The percentage error in resistivity of the material of the wire is

Q 9 :

The maximum percentage error in the measurement of density of a wire is

[Given, mass of wire = (0.60 $\pm$ 0.003) g

radius of wire = (0.50 $\pm$ 0.01) cm

length of wire = (10.00 $\pm$ 0.05) cm] [2025]

Q 10 :

The energy of a system is given as $E (t) = α^{3} e^{- β t}$ , where t is the time and $β = 0.3 s^{- 1}$ . The error in the measurement of $α$ and t are 1.2% and 1.6%, respectively. At t = 5 s, maximum percentage error in the energy is [2025]

Q 11 :

A quantity Q is formulated as $X^{- 2} Y^{+ \frac{3}{2}} Z^{- \frac{2}{5}} \cdot X, Y$ , and Z are independent parameters which have fractional errors of 0.1, 0.2 and 0.5, respectively in measurement. The maximum fractional error of Q is [2025]

Q 12 :

A physical quantity Q is related to four observables a, b, c, d as follows:

$Q = \frac{a b^{4}}{c d} where, a = (60 \pm 3) P a; b = (20 \pm 0.1) m$ ,

$c = (40 \pm 0.2) {Nsm}^{- 2} and d = (50 \pm 0.1) m$ ,

then the percentage error in Q is $\frac{x}{1000}$ , where x = __________. [2025]

Q 13 :

A physical quantity C is related to four other quantities p, q, r and s as follows

$C = \frac{p q^{2}}{r^{3} \sqrt{s}}$

The percentage errors in the measurement of p, q, r and s are 1%, 2%, 3% and 2% respectively. The percentage error in the measurement of C will be __________ %. [2025]

Q 14 :

Two resistances are given as $R_{1} = (10 \pm 0.5) Ω$ and $R_{2} = (15 \pm 0.5) Ω$ . The percentage error in the measurement of equivalent resistance when they are connected in parallel is [2023]

Q 16 :

A cylindrical wire of mass (0.4 $\pm$ 0.01) g has length (8 $\pm$ 0.04) cm and radius (6 $\pm$ 0.03) cm. The maximum error in its density will be [2023]

Q 17 :

A physical quantity P is given as $P = \frac{a^{2} b^{3}}{c \sqrt{d}}$ . The percentage error in the measurement of a, b, c and d are 1%, 2%, 3% and 4% respectively. The percentage error in the measurement of quantity P will be [2023]

Q 18 :

A body of mass (5 $\pm$ 0.5) kg is moving with a velocity of (20 $\pm$ 0.4) m/s. Its kinetic energy will be [2023]

Q 19 :

Four persons measure the length of a rod as 20.00 cm, 19.75 cm, 17.01 cm, and 18.25 cm. The relative error in the measurement of average length of the rod is: [2026]

Q 20 :

In an experiment the values of two spring constants were measured as $k_{1} = (10 \pm 0.2) N/m$ and $k_{2} = (20 \pm 0.3) N/m$ . If these springs are connected in parallel, then the percentage error in the equivalent spring constant is: [2026]

Q 23 :

If E and H represent the intensity of electric field and magnetising field respectively, then the unit of E/H will be