Finding Significant Figures

Q. The. Vernier scale of an instrument has 50 divisions which coincides with 49 main scale divisions ..if each main scale division
Is 0.5 mm then using this instrument the minimum inaccuracy in the measurement of distance is

Ans is. 0.01mm

Q.

The percentage errors in the measurement of length and time period of a simple pendulum are $1\%and2\%$ respectively. Then, the maximum error in the measurement of the acceleration due to gravity is

1. $8\%$

2. $3\%$

3. $4\%$

4. $6\%$

5. $5\%$

Q. Pitch of a screw gauge is 1 mm and there are 50 divisions on circular scale. When screw gauge is completely closed ${28}^{th}$ division of circular scale coincides with reference line. When a sheet is placed in it, the linear scale reads 2 divisions and circular scale reads 16 divisions. Zero of linear scale is visible when screw gauge is completely closed. Thickness of the sheet is:

1. 1.76 mm
2. 2.12 mm
3. 2.88 mm
4. 32 mm

Q. Three students $S_1,S_2$ and $S_3$ perform an experiment for determining the acceleration due to gravity $\left(g\right)$ using a simple pendulum. They use different lengths of pendulum and record time for different number of oscillations. The observations are as shown in the table.

$\begin{array}{ccccc}\text{Student No.}& \text{Length of}& \text{No. of}& \text{Total time for}& \text{Time}\\ & \text{pendulum (cm)}& \text{oscillations (n)}& \text{n oscillations}& \text{period (s)}\\ 1.& 64.0& 8& 128.0& 16.0\\ 2.& 64.0& 4& 64.0& 16.0\\ 3.& 20.0& 4& 36.0& 9.0\end{array}$
(Least count of length $=0.1\text{m}$
least count for time $=0.1\text{s}$
If $E_1,E_2$ and $E_3$ are the percentage errors in ${}^{\prime }{g}^{\prime }$ for students $1,2$ and $3$ respectively, then the minimum percentage error is obtained by student no.

1. $2$
2. Insufficient data.
3. $1$
4. 
   $3$

Q.

Each division on the main scale of a Vernier callipers is 1mm. Which of the following Vernier scales give the least count equal to 0.01mm ?

(A)9 mm divided into 100 divisions

(B)99 mm divided into 100 divisions

Q.

The density of ice is $918kg/m^3$ and that of seawater $1030kg/m^3$. An ice block floats in water with a portion of volume $9.18\times {10}^{-4}{m}^3$ below the surface of the water. Find the volume of the ice block.

Q.

To measure a quantity, the smaller the unit used, the smaller is the numerical value obtained.

1. True
2. False

Q.

Use the given digits without repetition and make the greatest and the smallest four-digit number.

$9,7,4,1$

Q.

Write the noun form of achive

Q.

What are SI units? How many SI units are defined for fundamental quantities?

Q. Taking into account the significant figures, what is the value of $9.99m+0.0099$m?

Q. How many significant figures are there in $0.310\times {10}^5\text{m}$ ?

1. $2$
2. $3$
3. $4$
4. $5$

Q.

How do you express $0.00000054$ in scientific notation?

Q.

Convert:

$4hm8dam$into $mm$

Q. The number of significant figures in $0.00210$ is

1. four
2. six
3. five
4. three

Q. State the number of significant figures in the following
a. $0.006{\text{m}}^2$
b. $2.65\times {10}^3\text{kg}$
c. $0.2309{\text{m}}^{-3}$
d. $6.320\text{J}$
e. $0.006032{\text{m}}^2$

1. (a) - 1 ; (b) - 3 ; (c) - 4 ; (d) - 4 ; (e) - 6
2. (a) - 1 ; (b) - 3 ; (c) - 4 ; (d) - 4 ; (e) - 4
3. (a) - 1 ; (b) - 3 ; (c) - 4 ; (d) - 3 ; (e) - 4
4. (a) - 1 ; (b) - 3 ; (c) - 4 ; (d) - 3 ; (e) - 6

Q. Statement 1: Two students measure the length of a stick as $1.3\text{m}$ and $1.30\text{m}$. Both the measurements are equally accurate.
Statement 2: The zero at the end of a measurement is always meaningless.

1. Only statement 1 is correct.
2. Only statement 2 is correct.
3. Both statements are correct.
4. Both statements are incorrect.

Q. A vernier callipers has its main scale of $10cm$ equally divided into $200$ equal parts. Its vernier scale of $25$ divisions coincides with $12mm$ on the main scale. The least count of the instrument is -

1. $0.001cm$
2. $0.002cm$
3. $0.020cm$
4. $0.010cm$

Q.

Find the volume of the sphere. Round your answer to the nearest tenth.

Q. What is parallax error ?​​​​

Q. Result of operation $(0.87+0.58)\times 1.06$ according to significant figures is

Q. How many significant figures should be present in the answer to the following calculation:-
$\frac{2.5\times 1.25\times 3.5}{2.01}$

Q. Which of the following length measurements is most precise and why?
a. $2.0cm$
b. $2.00cm$
c. $2.000cm$

Q. The mass and volume of a body are $4.237g$ and $2.5$ $c{m}^3$, respectively. The density of the material of the body in correct significant figures is

1. $1.6948gc{m}^{-3}$
2. $1.69gc{m}^{-3}$
3. $1.7gc{m}^{-3}$
4. $1.695gc{m}^{-3}$

Q. The diameter and height of a cylinder are measured by a meter scale to be $12.6\pm 0.1$ cm and $34.2\pm 0.1$ cm , respectively. What will be the value of its volume in appropriate significant figures?

1. $4260\pm 80{cm}^3$
2. $4264.4\pm 81.0{cm}^3$
3. $4300\pm 80{cm}^3$
4. $4264\pm 81{cm}^3$

Q. Assertion :The number 1.202 has four significant figures and the number 0.0024 has two significant figures. Reason: All the non zero digits are significant.

1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
2. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
3. Assertion is correct but Reason is incorrect
4. Both Assertion and Reason are incorrect

Q. A screw gauge has 50 divisions on its circular scale and its screw moves by 1 mm on turning it by two revolutions. When the flat end of the screw is in contact with the stud, the zero of circular scale lies below the baseline and 4th division of circular scale is in line with the baseline. Find the zero error of the screw gauge.

Q. How many significant figures are there in $0.310\times {10}^5\text{m}$ ?

1. $2$
2. $3$
3. $4$
4. $5$

Q. The number of significant figures in $1.217\times {10}^{-4}$ is

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

Q. The measured mass and volume of a body are $53.63g$ and $5.8{cm}^3$ respectively, with possible errors of $0.01g$ and $0.1{cm}^3$. The maximum percentage error in density is about:

1. $1.74\%$
2. $5\%$
3. $10\%$
4. $0.2\%$