QBManager

Units and Measurements

139868 In an experiment four quantities $a, b, c$ and $d$ are measured with percentage error $1 %, 2 %$ . $3 %$ and $4 %$ respectively. A quantity ' $P$ ' is calculated as $P = \frac{a^{3} b^{2}}{c d}$ . Then the percentage error in ' $P$ ' is

1

14 %

2

10 %

3

7 %

4

4 %

Explanation:

A Given that,
Percentage change in, $a (\frac{Δ a}{a} \times 100) = 1 %$
Percentage change in, $b (\frac{Δ b}{b} \times 100) = 2 %$
Percentage change in, $c (\frac{Δ c}{c} \times 100) = 3 %$
Percentage change in, $d (\frac{Δ d}{d} \times 100) = 4 %$
and $P = \frac{a^{3} b^{2}}{cd}$
Percentage change in $P =$ ?
$\frac{Δ P}{P} \times 100 = 3 (\frac{Δ a}{a} \times 100) + 2 (\frac{Δ b}{b} \times 100) + (\frac{Δ c}{c} \times 100)$
$+ (\frac{Δ d}{d} \times 100)$
$= 3 \times 1 % + 2 \times 2 % + 1 \times 3 % + 1 \times 4 %$
$= 3 % + 4 % + 3 % + 4 %$
$\frac{Δ P}{P} \times 100 = 14 %$
Percentage change in $P = 14 %$

AP EAMCET-28.04.2017

Units and Measurements

139869 The percentage errors in the measurement of mass and speed are $2 %$ and $3 %$ respectively. The error in kinetic energy obtained by measuring mass and speed, will be

1

12 %

2

10 %

3

8 %

4

2 %

Explanation:

C Given that,
$%$ error in mass $(m) = 2 %$
$%$ error in speed $(v) = 3 %$
$∵$ K.E. $= \frac{1}{2} {mv}^{2}$
taking log of both side
$\log E = 10 g m + 2 \log v$
Differentiating of both side
$\frac{Δ E}{E} = \frac{Δ M}{M} + \frac{Δ V}{V}$
$= (\frac{Δ m}{m} \times 100) + 2 (\frac{Δ v}{v} \times 100)$
$= 1 \times 2 % + 2 \times 3 %$
$= 2 % + 6 %$
$= 8 %$

AIPMT 1995

Units and Measurements

139870 The density of a cube is measured by measuring its mass and length of its sides. If the maximum error in the measurement of mass and length are $4 %$ and $3 %$ respectively, the maximum error in the measurement of density will be

1

7 %

2

9 %

3

12 %

4

13 %

Explanation:

D Given that,
$%$ error in mass $= 4 %$
$%$ error in length $= 3 %$
$∵$ Density $D = \frac{mass}{volume} = \frac{m}{L^{3}}$
$∴ \frac{Δ D}{D} \times 100 = (\frac{Δ m}{m} \times 100) + 3 (\frac{Δ L}{L} \times 100)$
$= 1 \times 4 % + 3 \times 3 %$
$= 4 % + 9 %$
max. error in measurement of density $= 13 %$

AIPMT 1996

Units and Measurements

139871 Resistance of a given wire is obtained by measuring the current flowing in it and the voltage difference applied across it. If the percentage errors in the measurement of the current and the voltage difference are $3 %$ each, then error in the value of resistance of the wire is

1

6 %

2 zero

3

1 %

4

3 %

Explanation:

A Given that,
$%$ error in Voltage $(V) = 3 %$
$%$ error in current $(I) = 3 %$
$∵ R = \frac{V}{I}$
$\frac{Δ R}{R} \times 100 = \frac{Δ V}{V} \times 100 + \frac{Δ I}{I} \times 100$
$\frac{Δ R}{R} \times 100 = 3 % + 3 %$
max. error in resistance of wire $= 6 %$

AIEEE 2012

Units and Measurements

139868 In an experiment four quantities $a, b, c$ and $d$ are measured with percentage error $1 %, 2 %$ . $3 %$ and $4 %$ respectively. A quantity ' $P$ ' is calculated as $P = \frac{a^{3} b^{2}}{c d}$ . Then the percentage error in ' $P$ ' is

1

14 %

2

10 %

3

7 %

4

4 %

Explanation:

A Given that,
Percentage change in, $a (\frac{Δ a}{a} \times 100) = 1 %$
Percentage change in, $b (\frac{Δ b}{b} \times 100) = 2 %$
Percentage change in, $c (\frac{Δ c}{c} \times 100) = 3 %$
Percentage change in, $d (\frac{Δ d}{d} \times 100) = 4 %$
and $P = \frac{a^{3} b^{2}}{cd}$
Percentage change in $P =$ ?
$\frac{Δ P}{P} \times 100 = 3 (\frac{Δ a}{a} \times 100) + 2 (\frac{Δ b}{b} \times 100) + (\frac{Δ c}{c} \times 100)$
$+ (\frac{Δ d}{d} \times 100)$
$= 3 \times 1 % + 2 \times 2 % + 1 \times 3 % + 1 \times 4 %$
$= 3 % + 4 % + 3 % + 4 %$
$\frac{Δ P}{P} \times 100 = 14 %$
Percentage change in $P = 14 %$

AP EAMCET-28.04.2017

Units and Measurements

139869 The percentage errors in the measurement of mass and speed are $2 %$ and $3 %$ respectively. The error in kinetic energy obtained by measuring mass and speed, will be

1

12 %

2

10 %

3

8 %

4

2 %

Explanation:

C Given that,
$%$ error in mass $(m) = 2 %$
$%$ error in speed $(v) = 3 %$
$∵$ K.E. $= \frac{1}{2} {mv}^{2}$
taking log of both side
$\log E = 10 g m + 2 \log v$
Differentiating of both side
$\frac{Δ E}{E} = \frac{Δ M}{M} + \frac{Δ V}{V}$
$= (\frac{Δ m}{m} \times 100) + 2 (\frac{Δ v}{v} \times 100)$
$= 1 \times 2 % + 2 \times 3 %$
$= 2 % + 6 %$
$= 8 %$

AIPMT 1995

Units and Measurements

139870 The density of a cube is measured by measuring its mass and length of its sides. If the maximum error in the measurement of mass and length are $4 %$ and $3 %$ respectively, the maximum error in the measurement of density will be

1

7 %

2

9 %

3

12 %

4

13 %

Explanation:

D Given that,
$%$ error in mass $= 4 %$
$%$ error in length $= 3 %$
$∵$ Density $D = \frac{mass}{volume} = \frac{m}{L^{3}}$
$∴ \frac{Δ D}{D} \times 100 = (\frac{Δ m}{m} \times 100) + 3 (\frac{Δ L}{L} \times 100)$
$= 1 \times 4 % + 3 \times 3 %$
$= 4 % + 9 %$
max. error in measurement of density $= 13 %$

AIPMT 1996

Units and Measurements

139871 Resistance of a given wire is obtained by measuring the current flowing in it and the voltage difference applied across it. If the percentage errors in the measurement of the current and the voltage difference are $3 %$ each, then error in the value of resistance of the wire is

1

6 %

2 zero

3

1 %

4

3 %

Explanation:

A Given that,
$%$ error in Voltage $(V) = 3 %$
$%$ error in current $(I) = 3 %$
$∵ R = \frac{V}{I}$
$\frac{Δ R}{R} \times 100 = \frac{Δ V}{V} \times 100 + \frac{Δ I}{I} \times 100$
$\frac{Δ R}{R} \times 100 = 3 % + 3 %$
max. error in resistance of wire $= 6 %$

AIEEE 2012

Units and Measurements

139868 In an experiment four quantities $a, b, c$ and $d$ are measured with percentage error $1 %, 2 %$ . $3 %$ and $4 %$ respectively. A quantity ' $P$ ' is calculated as $P = \frac{a^{3} b^{2}}{c d}$ . Then the percentage error in ' $P$ ' is

1

14 %

2

10 %

3

7 %

4

4 %

Explanation:

A Given that,
Percentage change in, $a (\frac{Δ a}{a} \times 100) = 1 %$
Percentage change in, $b (\frac{Δ b}{b} \times 100) = 2 %$
Percentage change in, $c (\frac{Δ c}{c} \times 100) = 3 %$
Percentage change in, $d (\frac{Δ d}{d} \times 100) = 4 %$
and $P = \frac{a^{3} b^{2}}{cd}$
Percentage change in $P =$ ?
$\frac{Δ P}{P} \times 100 = 3 (\frac{Δ a}{a} \times 100) + 2 (\frac{Δ b}{b} \times 100) + (\frac{Δ c}{c} \times 100)$
$+ (\frac{Δ d}{d} \times 100)$
$= 3 \times 1 % + 2 \times 2 % + 1 \times 3 % + 1 \times 4 %$
$= 3 % + 4 % + 3 % + 4 %$
$\frac{Δ P}{P} \times 100 = 14 %$
Percentage change in $P = 14 %$

AP EAMCET-28.04.2017

Units and Measurements

139869 The percentage errors in the measurement of mass and speed are $2 %$ and $3 %$ respectively. The error in kinetic energy obtained by measuring mass and speed, will be

1

12 %

2

10 %

3

8 %

4

2 %

Explanation:

C Given that,
$%$ error in mass $(m) = 2 %$
$%$ error in speed $(v) = 3 %$
$∵$ K.E. $= \frac{1}{2} {mv}^{2}$
taking log of both side
$\log E = 10 g m + 2 \log v$
Differentiating of both side
$\frac{Δ E}{E} = \frac{Δ M}{M} + \frac{Δ V}{V}$
$= (\frac{Δ m}{m} \times 100) + 2 (\frac{Δ v}{v} \times 100)$
$= 1 \times 2 % + 2 \times 3 %$
$= 2 % + 6 %$
$= 8 %$

AIPMT 1995

Units and Measurements

139870 The density of a cube is measured by measuring its mass and length of its sides. If the maximum error in the measurement of mass and length are $4 %$ and $3 %$ respectively, the maximum error in the measurement of density will be

1

7 %

2

9 %

3

12 %

4

13 %

Explanation:

D Given that,
$%$ error in mass $= 4 %$
$%$ error in length $= 3 %$
$∵$ Density $D = \frac{mass}{volume} = \frac{m}{L^{3}}$
$∴ \frac{Δ D}{D} \times 100 = (\frac{Δ m}{m} \times 100) + 3 (\frac{Δ L}{L} \times 100)$
$= 1 \times 4 % + 3 \times 3 %$
$= 4 % + 9 %$
max. error in measurement of density $= 13 %$

AIPMT 1996

Units and Measurements

139871 Resistance of a given wire is obtained by measuring the current flowing in it and the voltage difference applied across it. If the percentage errors in the measurement of the current and the voltage difference are $3 %$ each, then error in the value of resistance of the wire is

1

6 %

2 zero

3

1 %

4

3 %

Explanation:

A Given that,
$%$ error in Voltage $(V) = 3 %$
$%$ error in current $(I) = 3 %$
$∵ R = \frac{V}{I}$
$\frac{Δ R}{R} \times 100 = \frac{Δ V}{V} \times 100 + \frac{Δ I}{I} \times 100$
$\frac{Δ R}{R} \times 100 = 3 % + 3 %$
max. error in resistance of wire $= 6 %$

AIEEE 2012

Units and Measurements

139868 In an experiment four quantities $a, b, c$ and $d$ are measured with percentage error $1 %, 2 %$ . $3 %$ and $4 %$ respectively. A quantity ' $P$ ' is calculated as $P = \frac{a^{3} b^{2}}{c d}$ . Then the percentage error in ' $P$ ' is

1

14 %

2

10 %

3

7 %

4

4 %

Explanation:

A Given that,
Percentage change in, $a (\frac{Δ a}{a} \times 100) = 1 %$
Percentage change in, $b (\frac{Δ b}{b} \times 100) = 2 %$
Percentage change in, $c (\frac{Δ c}{c} \times 100) = 3 %$
Percentage change in, $d (\frac{Δ d}{d} \times 100) = 4 %$
and $P = \frac{a^{3} b^{2}}{cd}$
Percentage change in $P =$ ?
$\frac{Δ P}{P} \times 100 = 3 (\frac{Δ a}{a} \times 100) + 2 (\frac{Δ b}{b} \times 100) + (\frac{Δ c}{c} \times 100)$
$+ (\frac{Δ d}{d} \times 100)$
$= 3 \times 1 % + 2 \times 2 % + 1 \times 3 % + 1 \times 4 %$
$= 3 % + 4 % + 3 % + 4 %$
$\frac{Δ P}{P} \times 100 = 14 %$
Percentage change in $P = 14 %$

AP EAMCET-28.04.2017

Units and Measurements

139869 The percentage errors in the measurement of mass and speed are $2 %$ and $3 %$ respectively. The error in kinetic energy obtained by measuring mass and speed, will be

1

12 %

2

10 %

3

8 %

4

2 %

Explanation:

C Given that,
$%$ error in mass $(m) = 2 %$
$%$ error in speed $(v) = 3 %$
$∵$ K.E. $= \frac{1}{2} {mv}^{2}$
taking log of both side
$\log E = 10 g m + 2 \log v$
Differentiating of both side
$\frac{Δ E}{E} = \frac{Δ M}{M} + \frac{Δ V}{V}$
$= (\frac{Δ m}{m} \times 100) + 2 (\frac{Δ v}{v} \times 100)$
$= 1 \times 2 % + 2 \times 3 %$
$= 2 % + 6 %$
$= 8 %$

AIPMT 1995

Units and Measurements

139870 The density of a cube is measured by measuring its mass and length of its sides. If the maximum error in the measurement of mass and length are $4 %$ and $3 %$ respectively, the maximum error in the measurement of density will be

1

7 %

2

9 %

3

12 %

4

13 %

Explanation:

D Given that,
$%$ error in mass $= 4 %$
$%$ error in length $= 3 %$
$∵$ Density $D = \frac{mass}{volume} = \frac{m}{L^{3}}$
$∴ \frac{Δ D}{D} \times 100 = (\frac{Δ m}{m} \times 100) + 3 (\frac{Δ L}{L} \times 100)$
$= 1 \times 4 % + 3 \times 3 %$
$= 4 % + 9 %$
max. error in measurement of density $= 13 %$

AIPMT 1996

Units and Measurements

139871 Resistance of a given wire is obtained by measuring the current flowing in it and the voltage difference applied across it. If the percentage errors in the measurement of the current and the voltage difference are $3 %$ each, then error in the value of resistance of the wire is

1

6 %

2 zero

3

1 %

4

3 %

Explanation:

A Given that,
$%$ error in Voltage $(V) = 3 %$
$%$ error in current $(I) = 3 %$
$∵ R = \frac{V}{I}$
$\frac{Δ R}{R} \times 100 = \frac{Δ V}{V} \times 100 + \frac{Δ I}{I} \times 100$
$\frac{Δ R}{R} \times 100 = 3 % + 3 %$
max. error in resistance of wire $= 6 %$

AIEEE 2012

Explanation:

Explanation:

Explanation:

Explanation:

Question Bank Series

Explanation:

Explanation:

Explanation:

Explanation:

Explanation:

Explanation:

Explanation:

Explanation:

Explanation:

Explanation:

Explanation:

Explanation:

Question Bank Series