Error and Uncertainty

Q.

The period of oscillation of a simple pendulum is $T=2\pi \sqrt{\frac{L}{g}}$. Measured value of L is 20.0 cm known to 1 mm accuracy and time for 100 oscillation of the pendulum is found to be 90 s using wrist watch of 1 s resolution. The accuracy in the determination of g is:

1. 3%
2. 1%
3. 5%
4. 2%

Q.

The time period of a simple pendulum is given by $T=2\pi \sqrt{\frac{l}{g}}$ The measured value of the length of the pendulum is $10cm$ known to a $1mm$ accuracy. The time for $200$ oscillations of the pendulum is found to be $100$ seconds using a clock of $1s$ resolution. The percentage accuracy in the determination of $‘g’$ using this pendulum is $‘x’$. The value of $‘x’$ to the nearest integer is.

1. $5\%$

2. $4\%$

3. $3\%$

4. $2\%$

Q. The density of the material of a cube is measured by measuring its mass and length of its side. If the maximum error in the measurement of mass and the length are $3\%$ and $2\%$ respectively, the maximum error in the measurement of density is

1. $1\%$
2. $5\%$
3. $7\%$
4. $9\%$

Q. A faulty thermometer has its fixed points marked 5 and 95. When this thermometer reads 68, the correct temperature in Celsius is

1. 68°C
2. 66°C
3. 70°C
4. 72°C

Q. A physical quantity $z$ depends on four observables $a,b,c$ and $d$ , as $z=\frac{a^2{b}^{\left(2/3\right)}}{\sqrt{c}{d}^3}$. The percentages of error in the measurement of $a,b,c$ and $d$ are $2\%,1.5\%,4\%$ and $2.5\%$ respectively. The percentage of error in $z$ is

1. $12.25\%$
2. $16.5\%$
3. $13.5\%$
4. $14.5\%$

Q. In an experiment to find acceleration due to gravity $\left(g\right)$ using simple pendulum, time period of $0.5\text{s}$ is measured from time of $100$ oscillations with a watchof $1\text{s}$ resolution. If measured value of length is $10\text{cm}$ known to $1\text{mm}$ accuracy, the accuracy in the determination of $g$ is found to be $x$%. The value of $x$ is _________

Q. A thermometer graduated according to a linear scale reads a value $x_0$, when in contact with boiling water, and $\frac{x_0}{3}$, when in contact with ice. What is the temperature of an object in ${}^{\circ }\text{C}$, if this thermometer , in the contact with an object, reads $\frac{x_0}{2}$?

1. $25$
2. $35$
3. $40$
4. $60$

Q. The pitch and the number of divisions, on the circular scale for a given screw gauge are $0.5\text{mm}$ and $100$ respectively. When the screw gauge is fully tightened without any object, the zero of its circular scale lies $3$ division below the mean line. The readings of the main scale and the circular scale, for a thin sheet, are $5.5\text{mm}$ and $48$ respectively, the thickness of the sheet is

1. $\text{5.950 mm}$
2. $\text{5.725 mm}$
3. $\text{5.740 mm}$
4. $\text{5.755 mm}$

Q.

Define percentage error.

Q.

In an experiment, we measure quantities a, b and c; then x is calculated from the formula $x=\frac{a{b}^2}{c^3}$ . The percentage errors in a, b and c are $\pm 1\%$ , $\pm 3\%$ and $\pm 2\%$ respectively. The percentage error in $x$ can be

1. $\pm 1\%$
   
2. \$\pm 4\%$
3. $\pm 7\%$
4. $\pm 13\%$

Q. A physical quantity ${}^{\prime }{y}^{\prime }$ is represented by the formula $y=m^2{r}^{-4}{g}^x{l}^{-\frac{3}{2}}$. If the percentage errors found in $y,m,r,l$ and $g$ are $18,1,0.5,4$ and $p$ respectively, then find the value of $x$ and $p$

1. $5\text{and}\pm 2$
2. $4\text{and}\pm 3$
3. $\frac{16}{3}\text{and}\pm \frac{3}{2}$
4. $8\text{and}\pm 2$

Q. The bob of a swinging seconds pendulum (one whose time period is $2s$) has a small speed $v_0$ at its lowest point. Its height from this lowest point, $2.25s$ after passing through it is

1. $\frac{v_0^2}{4g}$
2. $\frac{9v_0^2}{4g}$
3. $\frac{v_0^2}{2g}$
4. $\frac{v_0^2}{g}$

Q. Find out the fractional error for the following measurements of diameter (in $\text{cm}$) of a wire : $2.620,2.625,2.628,2.630$ and $2.626$.

1. $1$
2. $0.001$
3. $0.1$
4. $0.01$

Q.

The least count of a stopwatch is generally _______.

Q. A screw gauge of pitch $0.5mm$ is used to measure the diameter of uniform wire of length $6.8cm$, the main scale reading is $1.5mm$ and circular scale reading is $7$. The calculated curved surface area of wire to appropriate significant figures is :
[Screw gauge has $50$ divisions on its circular scale]

1. $3.9c{m}^2$
2. $2.4c{m}^2$
3. $3.4c{m}^2$
4. $6.8c{m}^2$

Q. Student $A$ and Student $B$ used two screw gauges of equal pitch and $100$ circular divisions each, to measure the radius of a given wire. The actual value of the radius of the wire is $0.322\text{cm}.$ The absolute value of the difference between the final circular scale readings observed by the students $A$ and $B$ is
[Figure shows position of reference ${}^{\prime }{O}^{\prime }$ when jaws of screw gauge are closed]
Given pitch = $0.1\text{cm}.$

Q. The percentage error in the measurement of mass and speed are $2\%$ and $3\%$ respectively. How much will be the maximum error in the estimation of the kinetic energy obtained by measuring mass and speed

1. $1\%$
2. $8\%$
3. $11\%$
4. $5\%$

Q. The time period (in $\text{s}$) of oscillations of a simple pendulum in an experiment is recorded as $2.36,2.65,2.24,2.17$ and $2.08$. The mean absolute error of the measurements is

1. $0.3\text{s}$
2. $0.164\text{s}$
3. $0.16\text{s}$
4. $0.2\text{s}$

Q.

What is difference between error and uncertainty

Q. When $6$ identical cells of no internal resistance are connected in series in the secondary circuit of a potentiometer, the balancing length is $l$, balancing length becomes $\frac{l}{3}$ when some cells are connected wrongly are

1. $2$
2. $1$
3. $4$
4. $3$

Q. Random error can be eliminated by

1. taking large number of observations and then their mean
2. eliminating the cause.
3. measuring the quantity with more than one instrument.
4. careful observation.

Q. Two quantities X1 = (3.0 plus or minus 0.1) S.I. units X2 = (6.0 plus or minus 0.2) S.I. units are given and they are combined so that we find value of combination by X = X1 + X2 and X = (X1.X2)/(X1+X2) then (1)find the smaller of the two combinations and (2) Relative error in smaller value of combinations

Q.

While measuring the length of a knitting needle, the reading of the scale at one end is $3.0\mathrm{cm}$ and at the other end is$33.1\mathrm{cm}$. What is the length of the needle?

Q. Find the equivalent resistance of the infinite ladder circuit shown in figure across terminal <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> $\text{A}$ and $\text{B}$.

1. $\frac{1+\sqrt{11}}{2}\Omega$
2. $\frac{2+\sqrt{22}}{2}\Omega$
3. $\frac{3+\sqrt{33}}{2}\Omega$
4. $\frac{8+\sqrt{39}}{5}\Omega$

Q. In a measurement, both positive and negative errors are found to occur with equal probability. The type of error is known as

1. Proportional error
2. Systematic error
3. Determinate error
4. Random error

Q. The pitch of a screw gauge is 0.5 mm and there are 100 divisions on its circular scale. The instrument reads +2 circular scale divisions when nothing is put in-between its jaws. In measuring the diameter of a wire, there are 8 divisions on the main scale and ${83}^{rd}$ circular scale division coincides with the reference line. Then the diameter of the wire is:

1. 4.05 mm
2. 4.405 mm
3. 3.05 mm
4. 1.25 mm

Q.

How many divisions are there on a Vernier scale?

Q. The radius of a sphere is $(6.3\pm 0.1)\text{cm}$. The percentage error in its volume is

1. $\frac{0.1}{6.3}\times 100$
2. $3\times \frac{0.1}{6.3}\times 100$
3. $\frac{0.1\times 100}{3.53}$
4. $3+(\frac{0.1}{5.3}\times 100)$

Q.

Name the instrument which can accurately measure the thickness of a paper.

Q. In case of measurement of $\text{'}g\text{'}$, if error in measurement of length of pendulum is $2\%$, the percentage error in time period is $1\%$. The maximum error in measurement of $g$ is

1. $1\%$
2. $2\%$
3. $4\%$
4. No error