Text Book Back Questions and Answers - Chapter 1 Nature of Physical World and Measurement 11th Science Guide Samacheer Kalvi Solutions - SaraNextGen [2024-2025]

Updated On May 15, 2024

By SaraNextGen

Nature of Physical World and Measurement

Multiple Choice Questions
Question 1.
One of the combinations from the fundamental physical constants is $\frac{h c}{\mathrm{G}}$. The unit of this expression is
(a) $\mathrm{Kg}^2$
(b) $\mathrm{m}^3$
(c) $\mathrm{S}^{-1}$
(d) $\mathrm{m}$
Answer:
(a) $\mathrm{Kg}^2$
Question 2.
If the error in the measurement of radius is $2 \%$, then the error in the determination of volume of the sphere will be
(a) $8 \%$
(b) $2 \%$
(c) $4 \%$
(d) $6 \%$
Answer:
(d) $6 \%$
Question 3.

If the length and time period of an oscillating pendulum have errors of $1 \%$ and $3 \%$ respectively then the error in measurement of acceleration due to gravity is 
(a) $4 \%$
(b) $5 \%$
(c) $6 \%$
(d) $7 \%$

Answer:
(d) $7 \%$
Question 4.
The length of a body is measured as $3.51 \mathrm{~m}$, if the accuracy is $0.01 \mathrm{~mm}$, then the percentage error in the measurement is ......
(a) $351 \%$
(b) $1 \%$
(c) $0.28 \%$
(d) $0.035 \%$
Answer:
(c) $0.28 \%$
Question 5.
Which of the following has the highest number of significant figures?
(a) $0.007 \mathrm{~m}^2$
(b) $2.64 \times 1024 \mathrm{~kg}$
(c) $0.0006032 \mathrm{~m}^2$
(d) $6.3200 \mathrm{~J}$
Answer:
(d) $6.3200 \mathrm{~J}$
Question 6.
If $\pi=3.14$, then the value of $\pi^2$ is .....
(a) 9.8596
(b) 9.860
(c) 9.86
(d) 9.9
Answer:
(c) 9.86
Question 7.
Which of the following pairs of physical quantities have same dimension?
(a) force and power
(b) torque and energy
(c) torque and power
(d) force and torque
Answer:
(b) torque and energy
Question 8.
The dimensional formula of Planck's constant $h$ is 

(a) $\left[\mathrm{ML}^2 \mathrm{~T}^{-1}\right]$
(b) $\left[\mathrm{ML}^2 \mathrm{~T}^{-3}\right]$
(c) $\left[\mathrm{MLTT}^{-1}\right]$
(d) $\left[\mathrm{MLTT}^{3-3}\right]$
Answer:
(a) $\left[\mathrm{ML}^2 \mathrm{~T}^{-1}\right]$
Question 9.
The velocity of a particle $\mathrm{v}$ at an instant $t$ is given by $\mathrm{v}=a t+b t^2$. The dimensions of $\mathrm{b}$ is .....
(a) $[\mathrm{L}]$
(b) $\left[\mathrm{LT}^{-1}\right]$
(c) $\left[\mathrm{LT}^{-2}\right]$
(d) $\left[\mathrm{LT}^{-3}\right]$
Answer:
(d) $\left[\mathrm{LT}^{-3}\right]$
Question 10.
The dimensional formula for gravitational constant $\mathrm{G}$ is [Related to AIPMT 2004]
(a) $\left[\mathrm{ML}^{-3} \mathrm{~T}^{-2}\right]$
(b) $\left[\mathrm{M}^{-1} \mathrm{~L}^3 \mathrm{~T}^{-2}\right]$
(c) $\left[\mathrm{M}^{-1} \mathrm{~L}^{-3} \mathrm{~T}^{-2}\right]$
(d) $\left[\mathrm{ML}^{-3} \mathrm{~T}^2\right]$
Answer:
(b) $\left[\mathrm{M}^{-1} \mathrm{~L}^3 \mathrm{~T}^{-2}\right]$
Question 11.
The density of a material in CGS system of units is $4 \mathrm{~g} \mathrm{~cm}^{-3}$. In a system of units in which unit of length is $10 \mathrm{~cm}$ and unit of mass is $100 \mathrm{~g}$, then the value of density of material will be

(a) 0.04
(b) 0.4
(c) 40
(d) 400
Answer:
(c) 40
Question 12.
If the force is proportional to square of velocity, then the dimension of proportionality constant is $[\mathrm{JEE}-2000] \ldots \ldots$
(a) $\left[\mathrm{MLT}^0\right]$
(b) $\left[\mathrm{MLT}^{-1}\right]$
(c) $\left[\mathrm{ML}^{-2} \mathrm{~T}\right]$
(d) $\left[\mathrm{ML}^{-1} \mathrm{~T}^0\right]$
Answer:
(d) $\left[\mathrm{ML}^{-1} \mathrm{~T}^0\right.$

Question 13.
The dimension of $\left(\mu_0 \varepsilon_0\right)^{\frac{1}{2}}$ is
(a) length
(b) time
(c) velocity
(d) force
Answer:
(c) velocity
Question 14.
Planck's constant (h), speed of light in vaccum (c) and Newton's gravitational constant (G) are taken as three fundamental constants. Which of the following combinations of these has the dimension of length? 
(a) $\frac{\sqrt{h \mathrm{G}}}{c^{\frac{3}{2}}}$
(b) $\frac{\sqrt{h \mathrm{G}}}{c^{\frac{5}{2}}}$
(c) $\sqrt{\frac{h c}{\mathrm{G}}}$
(d) $\sqrt{\frac{G c}{h^{\frac{3}{2}}}}$
Answer:
(a) $\frac{\sqrt{h \mathrm{G}}}{c^{\frac{3}{2}}}$
Question 15.
A length-scale (1) depends on the permittivity $(\varepsilon)$ of a dielectric material, Boltzmann constant $\left(\mathrm{k}_{\mathrm{B}}\right)$, the absolute temperature $(\mathrm{T})$, the number per unit volume $(\mathrm{n})$ of certain charged particles, and the charge (q) carried by each of the particles. Which of the following expression for 1 is dimensionally correct?. 
(a) $l=\sqrt{\frac{n q^2}{\varepsilon k_{\mathrm{B}} \mathrm{T}}}$
(b) $l=\sqrt{\frac{\varepsilon k_{\mathrm{B}} \mathrm{T}}{n q^2}}$
(c) $l=\sqrt{\frac{q^2}{\varepsilon n^{\frac{2}{3}} k_{\mathrm{B}} \mathrm{T}}}$
(d) $l=\sqrt{\frac{q^2}{\varepsilon n k_1}}$
Answer:
(b) $l=\sqrt{\frac{\varepsilon k_{\mathrm{B}} \mathrm{T}}{n q^2}}$

Short Answer Questions
Question 1.
Briefly explain the types of physical quantities.
Answer:
Physical quantities are classified into two types. There are fundamental and derived quantities. Fundamental or base quantities are quantities which cannot be expressed in terms of any other physical quantities. These are length, mass, time, electric current, temperature, luminous intensity and amount of substance.
Quantities that can be expressed in terms of fundamental quantities are called derived quantities. For example, area, volume, velocity, acceleration, force.
Question 2.
How will you measure the diameter of the Moon using parallax method?
Answer:
Let $\theta$ is the angular diameter of moon
$\mathrm{d}$ - is the distance of moon from earth, from figure, $\theta=\frac{\mathrm{D}}{d}$

Diameter of moon $\mathrm{D}=\mathrm{d} . \theta$
by knowing $\theta, \mathrm{d}$, diameter of moon can be calculated
Question 3.
Write the rules for determining significant figures.
Answer:
Rules for counting significant figures:

Note: 1 Multiplying or dividing factors, which are neither rounded numbers nor numbers representing measured values, are exact and they have infinite numbers of significant figures as per the situation.
For example, circumference of circle $\mathrm{S}=2 \pi \mathrm{r}$, Here the factor 2 is exact number. It can be written as $2.0,2.00$ or 2.000 as required.
Note: 2 The power of 10 is irrelevant to the determination of significant figures.
For example $\mathrm{x}=5.70 \mathrm{~m}=5.70 \times 10^2 \mathrm{~cm}=5.70 \times 10^3 \mathrm{~mm}=5.70 \times 10^{-3} \mathrm{~km}$.
In each case the number of significant figures is three.
Question 4.
What are the limitations of dimensional analysis?
Answer:
Limitations of Dimensional analysis
1. This method gives no information about the dimensionless constants in the formula like 1 , $2, \ldots \ldots \ldots \pi, e$, etc.
This method cannot decide whether the given quantity is a vector or a scalar.
This method is not suitable to derive relations involving trigonometric, exponential and logarithmic functions.
It cannot be applied to an equation involving more than three physical quantities.
It can only check on whether a physical relation is dimensionally correct but not the
correctness of the relation. For example, using dimensional analysis, $s=u t+\frac{1}{3} a t^2$ is
dimensionally correct whereas the correct relation is $s=u \mathrm{t}+\frac{1}{2} a t^2$

Question 5.
Define precision and accuracy. Explain with one example.
Answer:
The accuracy of a measurement is a measure of how close the measured value is to the true value of the quantity. Precision of a measurement is a closeness of two or more measured values to each other.
The true value of a certain length is near $5.678 \mathrm{~cm}$. In one experiment, using a measuring instrument of resolution $0.1 \mathrm{~cm}$, the measured value is found to be $5.5 \mathrm{~cm}$. In another experiment using a measuring instrument of greater resolution, say $0.01 \mathrm{~cm}$, the length is found to be $5.38 \mathrm{~cm}$. We find that the first measurement is more accurate as it is closer to the true value, but it has lesser precision. On the contrary, the second measurement is less accurate, but it is more precise.
LongAnswer Questions
Question 1.
(i) Explain the use of screw gauge and vernier caliper in measuring smaller distances. Answer:
(i) Measurement of small distances: screw gauge and vernier caliper Screw gauge:
The screw gauge is an instrument used for measuring accurately the dimensions of objects up to a maximum of about $50 \mathrm{~mm}$. The principle of the instrument is the magnification of linear motion using the circular motion of a screw. The least count of the screw gauge is $0.01 \mathrm{~mm}$. Vernier caliper: A vernier caliper is a versatile instrument for measuring the dimensions of an object namely diameter of a hole, or a depth of a hole. The least count of the vernier caliper is $0.1 \mathrm{~mm}$.

(ii) Write a note on triangulation method and radar method to measure larger distances.
Triangulation method for the height of an accessible object;
Let $\mathrm{AB}=\mathrm{h}$ be the height of the tree or tower to be measured. Let $\mathrm{C}$ be the point of observation at distance $\mathrm{x}$ from $\mathrm{B}$. Place a range finder at $\mathrm{C}$ and measure the angle of elevation, $\mathrm{ACB}=$
$\theta$ as shown in figure.
From right angled triangle $\mathrm{ABC}$,

$
\tan \theta=\frac{\mathrm{AB}}{\mathrm{BC}}=\frac{h}{x}
$
(or) height $\mathrm{h}=\mathrm{x} \tan \theta$
Knowing the distance $\mathrm{x}$, the height $\mathrm{h}$ can be determined.
RADAR method
The word RADAR stands for radio detection and ranging. A radar can be used to measure accurately the distance of a nearby planet such as Mars. In this method, radio waves are sent from transmitters which, after reflection from the planet, are detected by the receiver. By measuring, the time interval $(\mathrm{t})$ between the instants the radio waves are sent and received, the distance of the planet can be determined as where $\mathrm{v}$ is the speed of the radio wave. As the time taken ( $\mathrm{t}$ ) is for the distance covered during the forward and backward path of the radio waves, it is divided by 2 to get the actual distance of the object. This method can also be used to determine the height, at which an aeroplane flies from the ground.
$
d=\frac{v \times t}{2}
$
Speed $=$ distance travelled $/$ time taken
Distance $(d)=$ Speed of radio waves $\times$ time taken
Question 2.
Explain in detail the various types of errors.
Answer:
The uncertainty in a measurement is called an error. Random error, systematic error and gross error are the three possible errors.
(i) Systematic errors: Systematic errors are reproducible inaccuracies that are consistently * , in the same direction. These occur often due to a problem that persists throughout the experiment. Systematic errors can be classified as follows
(1) Instrumental errors: When an instrument is not calibrated properly at the time of

manufacture, instrumental errors may arise. If a measurement is made with a meter scale whose end is worn out, the result obtained will have errors. These errors can be corrected by choosing the instrument carefully.
(2) Imperfections in experimental technique or procedure: These errors arise due to the limitations in the experimental arrangement. As an example, while performing experiments with a calorimeter, if there is no proper insulation, there will be radiation losses. This results in errors and to overcome these, necessary correction has to be applied
(3) Personal errors: These errors are due to individuals performing the experiment, may be due to incorrect initial setting up of the experiment or carelessness of the individual making the observation due to improper precautions.
(4) Errors due to external causes: The change in the external conditions during an experiment can cause error in measurement. For example, changes in temperature, humidity, or pressure during measurements may affect the result of the measurement.
(5) Least count error: Least count is the smallest value that can be measured by the measuring instrument, and the error due to this measurement is least count error. The instrument's resolution hence is the cause of this error. Least count error can be reduced by using a high precision instrument for the measurement.
(ii) Random errors: Random errors may arise due to random and unpredictable variations in experimental conditions like pressure, temperature, voltage supply etc. Errors may also be due to personal errors by the observer who performs the experiment. Random errors are sometimes called "chance error". When different readings are obtained by a person every time he repeats the experiment, personal error occurs. For example, consider the case of the thickness of a wire measured using a screw gauge. The readings taken may be different for different trials. In this case, a large number of measurements are made and then the arithmetic mean is taken.
If $\mathrm{n}$ number of trial readings are taken in an experiment, and the readings are $a_1, a_2, a_3, \ldots \ldots \ldots \ldots \ldots \ldots \ldots . a_n$. The arithmetic mean is

Question 3.
What do you mean by propagation of errors? Explain the propagation of errors in addition and multiplication.
Answer:
A number of measured quantities may be involved in the final calculation of an experiment. Different types of instruments might have been used for taking readings. Then we may have to look at the errors in measuring various quantities, collectively.
The error in the final result depends on
(i) The errors in the individual measurements
(ii) On the nature of mathematical operations performed to get the final result. So we should know the rules to combine the errors.
The various possibilities of the propagation or combination of errors in different mathematical
operations are discussed below:
(i) Error in the sum of two quantities
Let $\triangle \mathrm{A}$ and $\Delta \mathrm{B}$ be the absolute errors in the two quantities $\mathrm{A}$ and $\mathrm{B}$ respectively. Then,
Measured value of $A=A \pm \Delta A$
Measured value of $B=B \pm \Delta B$
Consider the sum, $\mathrm{Z}=\mathrm{A}+\mathrm{B}$
The error $\Delta \mathrm{Z}$ in $\mathrm{Z}$ is then given by

The maximum possible error in the sum of two quantities is equal to the sum of the absolute errors in the individual quantities.
Error in the product of two quantities: Let $\triangle \mathrm{A}$ and $\Delta \mathrm{B}$ be the absolute errors in the two quantities $A$, and $B$, respectively. Consider the product $Z=A B$
The error $\Delta \mathrm{Z}$ in $\mathrm{Z}$ is given by $\mathrm{Z} \pm \Delta \mathrm{Z}=(\mathrm{A} \pm \Delta \mathrm{A})(\mathrm{B} \pm \Delta \mathrm{B})$ $=(\mathrm{AB}) \pm(\mathrm{A} \Delta \mathrm{B}) \pm(\mathrm{B} \Delta \mathrm{A}) \pm(\Delta \mathrm{A} \cdot \Delta \mathrm{B})$
Dividing L.H.S by $\mathrm{Z}$ and R.H.S by $\mathrm{AB}$, we get, $1 \pm \frac{\Delta \mathrm{Z}}{\mathrm{Z}}=1 \pm \frac{\Delta \mathrm{B}}{\mathrm{B}} \pm \frac{\Delta \mathrm{A}}{\mathrm{A}} \pm \frac{\Delta \mathrm{A}}{\mathrm{A}} \cdot \frac{\Delta \mathrm{B}}{\mathrm{B}}$
$
\frac{\Delta \mathrm{A}}{\mathrm{A}} \cdot \frac{\Delta \mathrm{B}}{\mathrm{B}}
$
As $\triangle \mathrm{A} / \mathrm{A}, \Delta \mathrm{B} / \mathrm{B}$ are both small quantities, their product term The maximum fractional error in $\mathrm{Z}$ is
$
\frac{\Delta \mathrm{Z}}{\mathrm{Z}}= \pm\left(\frac{\Delta \mathrm{A}}{\mathrm{A}}+\frac{\Delta \mathrm{B}}{\mathrm{B}}\right)
$
Question 4.
Write short note on the following:
(a) Unit
(b) Rounding - off
(c) Dimensionless quantities
Answer:
(a) Unit: An arbitrarily chosen standard of measurement of a quantity, which is accepted internationally is called unit of the quantity.
The units in which the fundamental quantities are measured are called fundamental or base units and the units of measurement of all other physical quantities, which can be obtained by a suitable multiplication or division of powers of fundamental units, are called derived units.
(b) Rounding - off: In no case should the result have more significant figures than die figures involved in the data used for calculation. The result of calculation with numbers containing more than one uncertain digit should be rounded off. The rules for rounding off are given below.

(c) Dimensionless quantities: On the basis of dimension, dimensionless quantities are classified into two categories.
(i) Dimensionless variables:
Physical quantities which have no dimensions, but have variable values are called dimensionless variables. Examples are specific gravity, strain, refractive index etc.
(ii) Dimensionless Constant:
Quantities which have constant values and also have no dimensions are called dimensionless constants. Examples are $\pi$, e, numbers etc.
Question 5.
Explain the principle of homogeniety of dimensions. What are its uses? Give example.
Answer:
The principle of homogeneity of dimensions states that the dimensions of all the terms in a physical expression should be the same. For example, in the physical expression $\mathrm{v}^2=\mathrm{u}^2+$ 2as, the dimensions of $\mathrm{v}^2, \mathrm{u}^2$ and 2 as are the same and equal to $\left[\mathrm{L}^2 \mathrm{~T}^{-2}\right]$.
(i) To convert a physical quantity from one system of units to another: This is based on the fact that the product of the numerical values (n) and its corresponding unit (u) is a constant, i.e, $=$ constant $\mathrm{n}_1\left[\mathrm{u}_1\right]=$ constant (or) $\mathrm{n}_1\left[\mathrm{u}_1\right]=\mathrm{n}_2\left[\mathrm{u}_2\right]$.
Consider a physical quantity which has dimension ' $a$ ' in mass, ' $b$ ' in length and ' $c$ ' in time. If the fundamental units in one system are $\mathrm{M}_1, \mathrm{~L}_1$ and $\mathrm{T}_1$ and the other system are $\mathrm{M}_2, \mathrm{~L}_2$ and $\mathrm{T}_2$ respectively, then we can write, $n_1\left[\mathrm{M}_1^a \mathrm{~L}_1^b \mathrm{~T}_1^c\right]=n_2\left[\mathrm{M}_2^a \mathrm{~L}_2^b \mathrm{~T}_2^c\right]$
We have thus converted the numerical value of physical quantity from one system of units into the other system.

Example: Convert $76 \mathrm{~cm}$ of mercury pressure into $\mathrm{Nm}^{-2}$ using the method of dimensions.
Solution:

In cgs system $76 \mathrm{~cm}$ of mercury pressure $=76 \times 13.6 \times 980$ dyne $\mathrm{cm}^{-2}$ The dimensional formula of pressure $\mathrm{P}$ is $\left[\mathrm{ML}^{-1} \mathrm{~T}^{-2}\right]$
(ii) To check the dimensional correctness of a given physical equation:
Example: The equation $\frac{1}{2} m v^2=\mathrm{mgh}$ can be checked by using this method as follows.
Solution:

Dimensional formula for
$
\frac{1}{2} m v^2=[\mathrm{M}]\left[\mathrm{LT}^{-1}\right]^2=\left[\mathrm{ML}^2 \mathrm{~T}^{-2}\right]
$
Dimensional formula for
$
\begin{aligned}
m g h & =[\mathrm{M}]\left[\mathrm{LT}^{-2}\right][\mathrm{L}]=\left[\mathrm{ML}^2 \mathrm{~T}^{-2}\right] \\
{\left[\mathrm{ML}^2 \mathrm{~T}^{-2}\right] } & =\left[\mathrm{ML}^2 \mathrm{~T}^{-2}\right]
\end{aligned}
$
Both sides are dimensionally the same, hence the equations
$
\frac{1}{2} m v^2=m g h
$
is dimensionally correct.
(iii) To establish the relation among various physical quantities:
Example: An expression for the time period $\mathrm{T}$ of a simple pendulum can be obtained by using this method as follows.
Let true period $\mathrm{T}$ depend upon
(i) mass $m$ of the bob
(ii) length 1 of the pendulum and
(iii) acceleration due to gravity $g$ at the place where the pendulum is suspended. Let the constant involved is $\mathrm{K}=2 \pi$.
Solution:
$
\begin{gathered}
\mathrm{T} \alpha \mathrm{m}^a l^b \mathrm{~g}^c \\
\mathrm{~T}=k \cdot m^a l^b \mathrm{~g}^c \\
\end{gathered}
$
Here $\mathrm{k}$ is the dimensionless constant. Rewriting the above equation with dimensions.
$
\begin{aligned}
{\left[\mathrm{T}^1\right] } & =\left[\mathrm{M}^a\right]\left[\mathrm{L}^b\right]\left[\mathrm{LT}^{-2}\right]^c \\
{\left[\mathrm{M}^0 \mathrm{~L}^0 \mathrm{~T}^1\right] } & =\left[\mathrm{M}^a \mathrm{~L}^{b+c} \mathrm{~T}^{-c}\right]
\end{aligned}
$
Comparing the powers of $\mathrm{M}, \mathrm{L}$ and $\mathrm{T}$ on both sides, $\mathrm{a}-0, \mathrm{~b}+\mathrm{c}=0,-2 \mathrm{c}=1$
Solving for $\mathrm{a}, \mathrm{b}$ and $\mathrm{c} \mathrm{a}=0, \mathrm{~b}=1 / 2$, and $\mathrm{c}=-1 / 2$
From the above equation
$
\begin{aligned}
& \mathrm{T}=\mathrm{k} \cdot \mathrm{m}^0 l^{1 / 2} g^{-1 / 2} \\
& \mathrm{~T}=k\left(\frac{l}{g}\right)^{1 / 2}=k \sqrt{l / g}
\end{aligned}
$
Experimentally $k=2 \pi$, hence
$
\mathrm{T}=2 \pi \sqrt{l / g}
$