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Units and Measurements

269251 A student performs an experiment for determination of $g [= \frac{4 π^{2} L}{T^{2}}], L \approx 1 m$ , and he commits an error of $Δ L$ for $T$ he tajes the time of $n$ oscillations with the stop watch of least count $Δ T$ . For which of the following data the measurement of $g$ will be most accurate?

1

Δ L = 0.5, Δ T = 0.1, n = 20

2

Δ L = 0.5, Δ T = 0.1, n = 50

3

Δ L = 0.5, Δ T = 0.01, n = 20

4

Δ L = 0.5, Δ T = 0.05, n = 50

Explanation:

$\frac{Δ g}{g} = \frac{Δ l}{l} + 2 \frac{Δ T}{T} (Δ l$ and $Δ T$ are least, and the number of readingsaremaximum)

Units and Measurements

269252 A rectangular metal slab of mass 33.333 has itslength $8.0 cm$ , breadth $5.0 cm$ and thickness $1 mm$ . The mass is measured with accuracy up to $1 mg$ with a sensitive balance. The length and breadth aremeasured with vernier calipers having a least count of $0.01 cm$ . The thickness is measured with a screw gauge of least count $0.01 mm$ . The percentage accuracy in density calculated from the above measurements is

1

13 %

2

130 %

3

1.6 %

4

16 %

Explanation:

Percertageerorgivespercertageacaracy $d = \frac{m}{l b h}$ relativeerror, $\frac{Δ d}{d} = \frac{Δ m}{m} + \frac{Δ l}{l} + \frac{Δ b}{b} + \frac{Δ h}{h}$ and calculate $(\frac{Δ d}{d}) \times 100$

Units and Measurements

269253 The initial and final temperatures are
recorded as $(40.6 \pm 0.3)^{\circ} C$ and $(50.7 \pm 0.2)^{\circ} C$ . Therise in temperature is

1

{10.1}^{\circ} C

2

(10.1 \pm 0.3)^{0} C

3

(10.1 \pm 0.5)^{0} C

4

(10.1 \pm 0.1)^{0} C

Explanation:

$t_{2} - t_{1} = (50.7 - 40.6) \pm (0.3 + 0.2)$

Units and Measurements

269254 In the measurement of a physical quantity $X = \frac{A^{2} B}{C^{1 / 3} D^{3}}$ . The percentageerrorsintroduced in themeasurements of thequantities $A, B, C$ and D are $2 %, 2 %, 4 %$ and $5 %$ respectively. Then theminimum amount of percentage of error in themeasurement of $X$ iscontributed by

1

A

2

B

3

C

4

D

Explanation:

$\frac{Δ X}{X} \times 100 = 2 \frac{Δ A}{A} \times 100 + \frac{Δ B}{B} \times 100$
$+ \frac{1}{3} \frac{Δ C}{C} \times 100 + \frac{3 Δ D}{D} \times 100$

Units and Measurements

269251 A student performs an experiment for determination of $g [= \frac{4 π^{2} L}{T^{2}}], L \approx 1 m$ , and he commits an error of $Δ L$ for $T$ he tajes the time of $n$ oscillations with the stop watch of least count $Δ T$ . For which of the following data the measurement of $g$ will be most accurate?

1

Δ L = 0.5, Δ T = 0.1, n = 20

2

Δ L = 0.5, Δ T = 0.1, n = 50

3

Δ L = 0.5, Δ T = 0.01, n = 20

4

Δ L = 0.5, Δ T = 0.05, n = 50

Explanation:

$\frac{Δ g}{g} = \frac{Δ l}{l} + 2 \frac{Δ T}{T} (Δ l$ and $Δ T$ are least, and the number of readingsaremaximum)

Units and Measurements

269252 A rectangular metal slab of mass 33.333 has itslength $8.0 cm$ , breadth $5.0 cm$ and thickness $1 mm$ . The mass is measured with accuracy up to $1 mg$ with a sensitive balance. The length and breadth aremeasured with vernier calipers having a least count of $0.01 cm$ . The thickness is measured with a screw gauge of least count $0.01 mm$ . The percentage accuracy in density calculated from the above measurements is

1

13 %

2

130 %

3

1.6 %

4

16 %

Explanation:

Percertageerorgivespercertageacaracy $d = \frac{m}{l b h}$ relativeerror, $\frac{Δ d}{d} = \frac{Δ m}{m} + \frac{Δ l}{l} + \frac{Δ b}{b} + \frac{Δ h}{h}$ and calculate $(\frac{Δ d}{d}) \times 100$

Units and Measurements

269253 The initial and final temperatures are
recorded as $(40.6 \pm 0.3)^{\circ} C$ and $(50.7 \pm 0.2)^{\circ} C$ . Therise in temperature is

1

{10.1}^{\circ} C

2

(10.1 \pm 0.3)^{0} C

3

(10.1 \pm 0.5)^{0} C

4

(10.1 \pm 0.1)^{0} C

Explanation:

$t_{2} - t_{1} = (50.7 - 40.6) \pm (0.3 + 0.2)$

Units and Measurements

269254 In the measurement of a physical quantity $X = \frac{A^{2} B}{C^{1 / 3} D^{3}}$ . The percentageerrorsintroduced in themeasurements of thequantities $A, B, C$ and D are $2 %, 2 %, 4 %$ and $5 %$ respectively. Then theminimum amount of percentage of error in themeasurement of $X$ iscontributed by

1

A

2

B

3

C

4

D

Explanation:

$\frac{Δ X}{X} \times 100 = 2 \frac{Δ A}{A} \times 100 + \frac{Δ B}{B} \times 100$
$+ \frac{1}{3} \frac{Δ C}{C} \times 100 + \frac{3 Δ D}{D} \times 100$

Units and Measurements

269251 A student performs an experiment for determination of $g [= \frac{4 π^{2} L}{T^{2}}], L \approx 1 m$ , and he commits an error of $Δ L$ for $T$ he tajes the time of $n$ oscillations with the stop watch of least count $Δ T$ . For which of the following data the measurement of $g$ will be most accurate?

1

Δ L = 0.5, Δ T = 0.1, n = 20

2

Δ L = 0.5, Δ T = 0.1, n = 50

3

Δ L = 0.5, Δ T = 0.01, n = 20

4

Δ L = 0.5, Δ T = 0.05, n = 50

Explanation:

$\frac{Δ g}{g} = \frac{Δ l}{l} + 2 \frac{Δ T}{T} (Δ l$ and $Δ T$ are least, and the number of readingsaremaximum)

Units and Measurements

269252 A rectangular metal slab of mass 33.333 has itslength $8.0 cm$ , breadth $5.0 cm$ and thickness $1 mm$ . The mass is measured with accuracy up to $1 mg$ with a sensitive balance. The length and breadth aremeasured with vernier calipers having a least count of $0.01 cm$ . The thickness is measured with a screw gauge of least count $0.01 mm$ . The percentage accuracy in density calculated from the above measurements is

1

13 %

2

130 %

3

1.6 %

4

16 %

Explanation:

Percertageerorgivespercertageacaracy $d = \frac{m}{l b h}$ relativeerror, $\frac{Δ d}{d} = \frac{Δ m}{m} + \frac{Δ l}{l} + \frac{Δ b}{b} + \frac{Δ h}{h}$ and calculate $(\frac{Δ d}{d}) \times 100$

Units and Measurements

269253 The initial and final temperatures are
recorded as $(40.6 \pm 0.3)^{\circ} C$ and $(50.7 \pm 0.2)^{\circ} C$ . Therise in temperature is

1

{10.1}^{\circ} C

2

(10.1 \pm 0.3)^{0} C

3

(10.1 \pm 0.5)^{0} C

4

(10.1 \pm 0.1)^{0} C

Explanation:

$t_{2} - t_{1} = (50.7 - 40.6) \pm (0.3 + 0.2)$

Units and Measurements

269254 In the measurement of a physical quantity $X = \frac{A^{2} B}{C^{1 / 3} D^{3}}$ . The percentageerrorsintroduced in themeasurements of thequantities $A, B, C$ and D are $2 %, 2 %, 4 %$ and $5 %$ respectively. Then theminimum amount of percentage of error in themeasurement of $X$ iscontributed by

1

A

2

B

3

C

4

D

Explanation:

$\frac{Δ X}{X} \times 100 = 2 \frac{Δ A}{A} \times 100 + \frac{Δ B}{B} \times 100$
$+ \frac{1}{3} \frac{Δ C}{C} \times 100 + \frac{3 Δ D}{D} \times 100$

Units and Measurements

269251 A student performs an experiment for determination of $g [= \frac{4 π^{2} L}{T^{2}}], L \approx 1 m$ , and he commits an error of $Δ L$ for $T$ he tajes the time of $n$ oscillations with the stop watch of least count $Δ T$ . For which of the following data the measurement of $g$ will be most accurate?

1

Δ L = 0.5, Δ T = 0.1, n = 20

2

Δ L = 0.5, Δ T = 0.1, n = 50

3

Δ L = 0.5, Δ T = 0.01, n = 20

4

Δ L = 0.5, Δ T = 0.05, n = 50

Explanation:

$\frac{Δ g}{g} = \frac{Δ l}{l} + 2 \frac{Δ T}{T} (Δ l$ and $Δ T$ are least, and the number of readingsaremaximum)

Units and Measurements

269252 A rectangular metal slab of mass 33.333 has itslength $8.0 cm$ , breadth $5.0 cm$ and thickness $1 mm$ . The mass is measured with accuracy up to $1 mg$ with a sensitive balance. The length and breadth aremeasured with vernier calipers having a least count of $0.01 cm$ . The thickness is measured with a screw gauge of least count $0.01 mm$ . The percentage accuracy in density calculated from the above measurements is

1

13 %

2

130 %

3

1.6 %

4

16 %

Explanation:

Percertageerorgivespercertageacaracy $d = \frac{m}{l b h}$ relativeerror, $\frac{Δ d}{d} = \frac{Δ m}{m} + \frac{Δ l}{l} + \frac{Δ b}{b} + \frac{Δ h}{h}$ and calculate $(\frac{Δ d}{d}) \times 100$

Units and Measurements

269253 The initial and final temperatures are
recorded as $(40.6 \pm 0.3)^{\circ} C$ and $(50.7 \pm 0.2)^{\circ} C$ . Therise in temperature is

1

{10.1}^{\circ} C

2

(10.1 \pm 0.3)^{0} C

3

(10.1 \pm 0.5)^{0} C

4

(10.1 \pm 0.1)^{0} C

Explanation:

$t_{2} - t_{1} = (50.7 - 40.6) \pm (0.3 + 0.2)$

Units and Measurements

269254 In the measurement of a physical quantity $X = \frac{A^{2} B}{C^{1 / 3} D^{3}}$ . The percentageerrorsintroduced in themeasurements of thequantities $A, B, C$ and D are $2 %, 2 %, 4 %$ and $5 %$ respectively. Then theminimum amount of percentage of error in themeasurement of $X$ iscontributed by

1

A

2

B

3

C

4

D

Explanation:

$\frac{Δ X}{X} \times 100 = 2 \frac{Δ A}{A} \times 100 + \frac{Δ B}{B} \times 100$
$+ \frac{1}{3} \frac{Δ C}{C} \times 100 + \frac{3 Δ D}{D} \times 100$