Error and Uncertainty

Q.

Calculate the least count of the screw gauge.

Q. A screw gauge gives the following readings when used to measure the diameter of a wire.
Main scale reading $:0\text{mm}$
Circular scale reading $:52$ divisions

Given that $1\text{mm}$ on main scale corresponds to $100$ divisions on the circular scale. The diameter of the wire from the above data is

1. $0.52\text{cm}$
2. $0.26\text{cm}$
3. $0.026\text{cm}$
4. $0.052\text{cm}$

Q.

In an experiment of simple pendulum time period measured was 50 sec for 25 vibration when the length of the simple pendulum was taken 100 cm. If the least count of stop watch is 0.1 s and that of meter scale is 0.1 cm. Calculate the maximum percentage error in the measurement of value of g.

1. 

2. 

3. none of these

4. 

Q. Accuracy of any measurement is determined by

1. mean absolute error
2. percentage error
3. relative error
4. arithmetic mean of given measurements

Q.

If there is an error of $\pm 0.04cm$ in the measurement of the diameter of a sphere, then the approximate percentage error in its volume, when the radius is $10cm$, is

1. $\pm 1.2$

2. $\pm 0.06$

3. $\pm 0.006$

4. $\pm 0.6$

Q.

The period of oscillation of a simple pendulum in the experiment is recorded as 2.63 s, 2.56 s, 2.42, 2.71 s and 2.80 s respectively. Find the average absolute error.

1. 0.12s

2. 0.11 s

3. 0.108 s

4. none of these

Q.

In a simple pendulum experiment for the determination of acceleration due to gravity $\left(g\right)$, time taken for $20$ oscillations is measured by using a watch of $1$ second least count. The mean value of time taken comes out to be $30s$. The length of the pendulum is measured by using a meter scale of least count $1mm$ and the value obtained is $55.0cm$. The percentage error in the determination of $g$ is close to

1. $0.7\%$

2. $0.2\%$

3. $3.5\%$

4. $6.8\%$

Q. what is the range of time scale ?

Q.

A micrometer screw gauge having a positive zero error of 5 divisions is used to measure the diameter of the wire, when reading on the main scale is the 3rd division, and the 48th circular scale division coincides with the baseline. If the micrometer has 10 divisions to a centimetre on the main scale and 100 divisions on the circular scale, calculate the observed diameter.

Q. The random error in the arithmetic mean of $100$ observations of a physical quantity is $x$, then random error in the arithmetic mean of $400$ observations of the same physical quantity will be

1. $\frac{x}{4}$
2. $\frac{x}{2}$
3. $4x$
4. $2x$

Q. Precise measurements of physical quantities are a need of science. For example, to ascertain the speed of an aircraft, one must have an accurate method to find its positions at closely separated instants of time. This was the actual motivation behind the discovery of radar in World War II. Think of different examples in modern science where precise measurements of length, time, mass etc. are needed. Also, wherever you can, give a quantitative idea of the precision needed.

Q. It is claimed that two cesium clocks, if allowed to run for 100 years, free from any disturbance, may differ by only about 0.02 s. What does this imply for the accuracy of the standard cesium clock in measuring a time-interval of 1 s ?

Q. 10. In serew gauge. the distance moved by screw on the linear scale is 10 mm in 10 complete rotation. There are 50 divisions onthe eircular scale. When nothing is put in between the studs, 45th division of the circular scale coincides with the referendeline. While measuring the thickness of glass plate, the main scale reads four divisions and circular scale reads 30 divisionsFind the thickness of the plate.(a) 9 mm(d) 4.6 mm(c) 11 mm(b) 10 mm

Q. Accuracy of any measurement is determined by

1. mean absolute error
2. percentage error
3. relative error
4. arithmetic mean of given measurements

Q.

The period of oscillation of a simple pendulum in the experiment is recorded as 2.63 s, 2.56 s, 2.42, 2.71 s and 2.80 s respectively. Find the average absolute error.

1. 0.12s

2. 0.11 s

3. 0.108 s

4. none of these

Q. The observations of measurement of length (in $\text{m}$) of a wooden stick are $1.22,1.23,1.23,1.24,$ and $1.25$ then the mean absolute error will be

1. $0.01\text{m}$
2. $0.1\text{m}$
3. $0.008\text{m}$
4. $0.08\text{m}$

Q. The mean time period of seconds pendulum is $2.00\text{s}$ and mean absolute error in the time period is $0.05\text{s}$. Any measurement of the time period will be

1. $>(2.00+0.05)\text{s}$
2. $<(2.00-0.05)\text{s}$
3. in the interval $(2.00\pm 0.05)\text{s}$
4. $2.00\text{s}$

Q. To measure the volume of a cylinderical wire, its diameter is measured by a screw gauge and is found to be 1.25 mm, and its length is measured with a vernier caliper and is found to be 5.50 cm. The least count of the screw gauge is 0.01 mm, and that of the vernier caliper is 0.01 cm.

1. Percentage error due to area is more than percentage error due to length.
2. Number of significant figures in volume will be two.
3. Percentage error in volume will be 1.78%.
4. Percentage error in length is 1.6%.

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

Q. 101. Why systematic error is always in either positive or in negative

Q.

Which team's measurements are more reliable?

1. Team A

2. Team B

3. Both are equally reliable

4. Both are unreliable

Q. The random error in the arithmetic mean of $100$ observations of a physical quantity is $x$, then random error in the arithmetic mean of $400$ observations of the same physical quantity will be

1. $\frac{x}{4}$
2. $\frac{x}{2}$
3. $4x$
4. $2x$

Q. Time period of 10 oscillations of a simple pendulum is found to be 20 sec by a stopwatch of resolution 0.25 sec. Length of the string is measured to be 30 cm by a scale of least count 0.1 cm. Percentage error in measurement of acceleration due to gravity g by simple pendulum is? $T=2\pi \sqrt{\frac{l}{g}}$

Q. If error in measurement of radius of sphere is $1\%$, what will be the error in measurement of volume?

1. $1\%$
2. $1/3\%$
3. $3\%$
4. $10\%$

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

Q. The observations of measurement of length (in $\text{m}$) of a wooden stick are $1.22,1.23,1.23,1.24,$ and $1.25$ then the mean absolute error will be

1. $0.01\text{m}$
2. $0.1\text{m}$
3. $0.008\text{m}$
4. $0.08\text{m}$

Q. The mean time period of seconds pendulum is $2.00\text{s}$ and mean absolute error in the time period is $0.05\text{s}$. Any measurement of the time period will be

1. $>(2.00+0.05)\text{s}$
2. $<(2.00-0.05)\text{s}$
3. in the interval $(2.00\pm 0.05)\text{s}$
4. $2.00\text{s}$

Q. The mean length of an object is $5\text{cm}$. Which of the following measurements is most accurate?

1. $4.90\text{cm}$
2. $4.85\text{cm}$
3. $4.80\text{cm}$
4. $4.75\text{cm}$

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

Q. For three capacitors of capacitance $2\mu \text{F}$, $4\mu \text{F}$, $8\mu \text{F}$ connected parallel to each other having applied voltages $20\text{V}$, $40\text{V}$, $60\text{V}$ respectively. Then the equivalent breakdown voltage of the combination is?

1. $60\text{V}$
2. $11.4\text{V}$
3. $20\text{V}$
4. $40\text{V}$