03. Errors
Units and Measurements

139885 The velocity of a transverse wave in a string is directly proportional to \(\sqrt{T}\) and inversely proportional to \(\sqrt{\mu}\). In a measurement, the mass applied at the end of string is \(3.0 \mathrm{gm}\), length of string is \(1 \mathrm{~m}\) and mass of string is 5 gm. If possible error in measuring mass is 0.1 \(\mathbf{g m}\) and that of length is \(1 \mathrm{~mm}\), the parentage error in measurement of velocity is

1 \(4.5 \%\)
2 \(2.7 \%\)
3 \(2.1 \%\)
4 \(3.7 \%\)
Units and Measurements

139886 A physical quantity \(Q\) is related to four observables \(x, y, z\) ad \(t\) by the relation
\(Q=\frac{x^{2 / 5} z^{3}}{y \sqrt{t}}\)
The percentage errors of measurement in \(x, y\), \(z\), and \(t\) are \(2.5 \%, 2 \%, 0.5 \%\) and \(1 \%\) respectively. The percentage error in \(Q\) will be

1 \(5 \%\)
2 \(4.5 \%\)
3 \(8 \%\)
4 \(7.75 \%\)
Units and Measurements

139888 What is the approximate percentage error in the measurement of time period of a simple pendulum if maximum errors in the measurement of length \(l\) and gravitational acceleration \(g\) are \(3 \%\) and \(7 \%\) respectively?

1 \(5 \%\)
2 \(10 \%\)
3 \(2 \%\)
4 \(3 \%\)
Units and Measurements

139889 The relation gives the value of \(x\) as \(x=\frac{\left(a^{3} b^{3}\right)}{(c \sqrt{d})}\)
Find the percentage error in \(x\), if the percentage error in a, b, c, d, are \(2 \%, 1 \%, 2 \%\) and \(4 \%\) respectively :

1 \(\pm 13 \%\)
2 \(\pm 5 \%\)
3 \(\pm 9 \%\)
4 \(\pm 8 \%\)
Units and Measurements

139890 When the voltage and current in a conductor are measured as \((100 \pm 4) \mathrm{V}\) and \((5 \pm 0.2) \mathrm{A}\), then the percentage of error in the calculation of resistance is

1 \(8 \%\)
2 \(4 \%\)
3 \(20 \%\)
4 \(10 \%\)
5 \(6 \%\)
Units and Measurements

139885 The velocity of a transverse wave in a string is directly proportional to \(\sqrt{T}\) and inversely proportional to \(\sqrt{\mu}\). In a measurement, the mass applied at the end of string is \(3.0 \mathrm{gm}\), length of string is \(1 \mathrm{~m}\) and mass of string is 5 gm. If possible error in measuring mass is 0.1 \(\mathbf{g m}\) and that of length is \(1 \mathrm{~mm}\), the parentage error in measurement of velocity is

1 \(4.5 \%\)
2 \(2.7 \%\)
3 \(2.1 \%\)
4 \(3.7 \%\)
Units and Measurements

139886 A physical quantity \(Q\) is related to four observables \(x, y, z\) ad \(t\) by the relation
\(Q=\frac{x^{2 / 5} z^{3}}{y \sqrt{t}}\)
The percentage errors of measurement in \(x, y\), \(z\), and \(t\) are \(2.5 \%, 2 \%, 0.5 \%\) and \(1 \%\) respectively. The percentage error in \(Q\) will be

1 \(5 \%\)
2 \(4.5 \%\)
3 \(8 \%\)
4 \(7.75 \%\)
Units and Measurements

139888 What is the approximate percentage error in the measurement of time period of a simple pendulum if maximum errors in the measurement of length \(l\) and gravitational acceleration \(g\) are \(3 \%\) and \(7 \%\) respectively?

1 \(5 \%\)
2 \(10 \%\)
3 \(2 \%\)
4 \(3 \%\)
Units and Measurements

139889 The relation gives the value of \(x\) as \(x=\frac{\left(a^{3} b^{3}\right)}{(c \sqrt{d})}\)
Find the percentage error in \(x\), if the percentage error in a, b, c, d, are \(2 \%, 1 \%, 2 \%\) and \(4 \%\) respectively :

1 \(\pm 13 \%\)
2 \(\pm 5 \%\)
3 \(\pm 9 \%\)
4 \(\pm 8 \%\)
Units and Measurements

139890 When the voltage and current in a conductor are measured as \((100 \pm 4) \mathrm{V}\) and \((5 \pm 0.2) \mathrm{A}\), then the percentage of error in the calculation of resistance is

1 \(8 \%\)
2 \(4 \%\)
3 \(20 \%\)
4 \(10 \%\)
5 \(6 \%\)
Units and Measurements

139885 The velocity of a transverse wave in a string is directly proportional to \(\sqrt{T}\) and inversely proportional to \(\sqrt{\mu}\). In a measurement, the mass applied at the end of string is \(3.0 \mathrm{gm}\), length of string is \(1 \mathrm{~m}\) and mass of string is 5 gm. If possible error in measuring mass is 0.1 \(\mathbf{g m}\) and that of length is \(1 \mathrm{~mm}\), the parentage error in measurement of velocity is

1 \(4.5 \%\)
2 \(2.7 \%\)
3 \(2.1 \%\)
4 \(3.7 \%\)
Units and Measurements

139886 A physical quantity \(Q\) is related to four observables \(x, y, z\) ad \(t\) by the relation
\(Q=\frac{x^{2 / 5} z^{3}}{y \sqrt{t}}\)
The percentage errors of measurement in \(x, y\), \(z\), and \(t\) are \(2.5 \%, 2 \%, 0.5 \%\) and \(1 \%\) respectively. The percentage error in \(Q\) will be

1 \(5 \%\)
2 \(4.5 \%\)
3 \(8 \%\)
4 \(7.75 \%\)
Units and Measurements

139888 What is the approximate percentage error in the measurement of time period of a simple pendulum if maximum errors in the measurement of length \(l\) and gravitational acceleration \(g\) are \(3 \%\) and \(7 \%\) respectively?

1 \(5 \%\)
2 \(10 \%\)
3 \(2 \%\)
4 \(3 \%\)
Units and Measurements

139889 The relation gives the value of \(x\) as \(x=\frac{\left(a^{3} b^{3}\right)}{(c \sqrt{d})}\)
Find the percentage error in \(x\), if the percentage error in a, b, c, d, are \(2 \%, 1 \%, 2 \%\) and \(4 \%\) respectively :

1 \(\pm 13 \%\)
2 \(\pm 5 \%\)
3 \(\pm 9 \%\)
4 \(\pm 8 \%\)
Units and Measurements

139890 When the voltage and current in a conductor are measured as \((100 \pm 4) \mathrm{V}\) and \((5 \pm 0.2) \mathrm{A}\), then the percentage of error in the calculation of resistance is

1 \(8 \%\)
2 \(4 \%\)
3 \(20 \%\)
4 \(10 \%\)
5 \(6 \%\)
Units and Measurements

139885 The velocity of a transverse wave in a string is directly proportional to \(\sqrt{T}\) and inversely proportional to \(\sqrt{\mu}\). In a measurement, the mass applied at the end of string is \(3.0 \mathrm{gm}\), length of string is \(1 \mathrm{~m}\) and mass of string is 5 gm. If possible error in measuring mass is 0.1 \(\mathbf{g m}\) and that of length is \(1 \mathrm{~mm}\), the parentage error in measurement of velocity is

1 \(4.5 \%\)
2 \(2.7 \%\)
3 \(2.1 \%\)
4 \(3.7 \%\)
Units and Measurements

139886 A physical quantity \(Q\) is related to four observables \(x, y, z\) ad \(t\) by the relation
\(Q=\frac{x^{2 / 5} z^{3}}{y \sqrt{t}}\)
The percentage errors of measurement in \(x, y\), \(z\), and \(t\) are \(2.5 \%, 2 \%, 0.5 \%\) and \(1 \%\) respectively. The percentage error in \(Q\) will be

1 \(5 \%\)
2 \(4.5 \%\)
3 \(8 \%\)
4 \(7.75 \%\)
Units and Measurements

139888 What is the approximate percentage error in the measurement of time period of a simple pendulum if maximum errors in the measurement of length \(l\) and gravitational acceleration \(g\) are \(3 \%\) and \(7 \%\) respectively?

1 \(5 \%\)
2 \(10 \%\)
3 \(2 \%\)
4 \(3 \%\)
Units and Measurements

139889 The relation gives the value of \(x\) as \(x=\frac{\left(a^{3} b^{3}\right)}{(c \sqrt{d})}\)
Find the percentage error in \(x\), if the percentage error in a, b, c, d, are \(2 \%, 1 \%, 2 \%\) and \(4 \%\) respectively :

1 \(\pm 13 \%\)
2 \(\pm 5 \%\)
3 \(\pm 9 \%\)
4 \(\pm 8 \%\)
Units and Measurements

139890 When the voltage and current in a conductor are measured as \((100 \pm 4) \mathrm{V}\) and \((5 \pm 0.2) \mathrm{A}\), then the percentage of error in the calculation of resistance is

1 \(8 \%\)
2 \(4 \%\)
3 \(20 \%\)
4 \(10 \%\)
5 \(6 \%\)
Units and Measurements

139885 The velocity of a transverse wave in a string is directly proportional to \(\sqrt{T}\) and inversely proportional to \(\sqrt{\mu}\). In a measurement, the mass applied at the end of string is \(3.0 \mathrm{gm}\), length of string is \(1 \mathrm{~m}\) and mass of string is 5 gm. If possible error in measuring mass is 0.1 \(\mathbf{g m}\) and that of length is \(1 \mathrm{~mm}\), the parentage error in measurement of velocity is

1 \(4.5 \%\)
2 \(2.7 \%\)
3 \(2.1 \%\)
4 \(3.7 \%\)
Units and Measurements

139886 A physical quantity \(Q\) is related to four observables \(x, y, z\) ad \(t\) by the relation
\(Q=\frac{x^{2 / 5} z^{3}}{y \sqrt{t}}\)
The percentage errors of measurement in \(x, y\), \(z\), and \(t\) are \(2.5 \%, 2 \%, 0.5 \%\) and \(1 \%\) respectively. The percentage error in \(Q\) will be

1 \(5 \%\)
2 \(4.5 \%\)
3 \(8 \%\)
4 \(7.75 \%\)
Units and Measurements

139888 What is the approximate percentage error in the measurement of time period of a simple pendulum if maximum errors in the measurement of length \(l\) and gravitational acceleration \(g\) are \(3 \%\) and \(7 \%\) respectively?

1 \(5 \%\)
2 \(10 \%\)
3 \(2 \%\)
4 \(3 \%\)
Units and Measurements

139889 The relation gives the value of \(x\) as \(x=\frac{\left(a^{3} b^{3}\right)}{(c \sqrt{d})}\)
Find the percentage error in \(x\), if the percentage error in a, b, c, d, are \(2 \%, 1 \%, 2 \%\) and \(4 \%\) respectively :

1 \(\pm 13 \%\)
2 \(\pm 5 \%\)
3 \(\pm 9 \%\)
4 \(\pm 8 \%\)
Units and Measurements

139890 When the voltage and current in a conductor are measured as \((100 \pm 4) \mathrm{V}\) and \((5 \pm 0.2) \mathrm{A}\), then the percentage of error in the calculation of resistance is

1 \(8 \%\)
2 \(4 \%\)
3 \(20 \%\)
4 \(10 \%\)
5 \(6 \%\)