ACCURACY,PRECISION,TYPESOF ERRORSAND COM BINATION OF ERRORS
Units and Measurements

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

1 \(\Delta L=0.5, \Delta T=0.1, n=20\)
2 \(\Delta L=0.5, \Delta T=0.1, n=50\)
3 \(\Delta L=0.5, \Delta T=0.01, n=20\)
4 \(\Delta L=0.5, \Delta T=0.05, n=50\)
Units and Measurements

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

1 \(13 \%\)
2 \(130 \%\)
3 \(1.6 \%\)
4 \(16 \%\)
Units and Measurements

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

1 \(10.1^{\circ} \mathrm{C}\)
2 \((10.1 \pm 0.3)^{0} \mathrm{C}\)
3 \((10.1 \pm 0.5)^{0} \mathrm{C}\)
4 \((10.1 \pm 0.1)^{0} \mathrm{C}\)
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 \(\mathrm{C}\)
4 \(D\)
Units and Measurements

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

1 \(\Delta L=0.5, \Delta T=0.1, n=20\)
2 \(\Delta L=0.5, \Delta T=0.1, n=50\)
3 \(\Delta L=0.5, \Delta T=0.01, n=20\)
4 \(\Delta L=0.5, \Delta T=0.05, n=50\)
Units and Measurements

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

1 \(13 \%\)
2 \(130 \%\)
3 \(1.6 \%\)
4 \(16 \%\)
Units and Measurements

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

1 \(10.1^{\circ} \mathrm{C}\)
2 \((10.1 \pm 0.3)^{0} \mathrm{C}\)
3 \((10.1 \pm 0.5)^{0} \mathrm{C}\)
4 \((10.1 \pm 0.1)^{0} \mathrm{C}\)
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 \(\mathrm{C}\)
4 \(D\)
Units and Measurements

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

1 \(\Delta L=0.5, \Delta T=0.1, n=20\)
2 \(\Delta L=0.5, \Delta T=0.1, n=50\)
3 \(\Delta L=0.5, \Delta T=0.01, n=20\)
4 \(\Delta L=0.5, \Delta T=0.05, n=50\)
Units and Measurements

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

1 \(13 \%\)
2 \(130 \%\)
3 \(1.6 \%\)
4 \(16 \%\)
Units and Measurements

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

1 \(10.1^{\circ} \mathrm{C}\)
2 \((10.1 \pm 0.3)^{0} \mathrm{C}\)
3 \((10.1 \pm 0.5)^{0} \mathrm{C}\)
4 \((10.1 \pm 0.1)^{0} \mathrm{C}\)
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 \(\mathrm{C}\)
4 \(D\)
Units and Measurements

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

1 \(\Delta L=0.5, \Delta T=0.1, n=20\)
2 \(\Delta L=0.5, \Delta T=0.1, n=50\)
3 \(\Delta L=0.5, \Delta T=0.01, n=20\)
4 \(\Delta L=0.5, \Delta T=0.05, n=50\)
Units and Measurements

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

1 \(13 \%\)
2 \(130 \%\)
3 \(1.6 \%\)
4 \(16 \%\)
Units and Measurements

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

1 \(10.1^{\circ} \mathrm{C}\)
2 \((10.1 \pm 0.3)^{0} \mathrm{C}\)
3 \((10.1 \pm 0.5)^{0} \mathrm{C}\)
4 \((10.1 \pm 0.1)^{0} \mathrm{C}\)
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 \(\mathrm{C}\)
4 \(D\)