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Physics 1 Marks Question

Units and Measurements · MP Board (MPBSE) STD 11 Science (Madhya Pradesh - English Medium). 149 questions.

Questions · Page 3 of 3

1 Marks Question

Question 1011 Mark
State dimensional formulae for stress, strain and Young's modulus.
Answer
Strain is dimensionless quantity. Dimensional formula for stress is $\left[\mathrm{ML}^{-1} \mathrm{~T}^{-2}\right]$ Young's modulus has same dimensional formula as stress i.e. $\left[\mathrm{ML}^{-1} \mathrm{~T}^{-2}\right]$
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Question 1021 Mark
What do you mean by order of magnitude? Explain.
Answer
The order of magnitude of a numerical quantity $(\mathrm{N})$ is the nearest power of 10 to which its value can be written. For example: Order of magnitude of nuclear radius $1.5 \times 10^{-14} \mathrm{~m}$ is -14 .
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Question 1031 Mark
Give the relationship between light year and metre.
Answer
1 light year $=9.467 \times 10^{15} \mathrm{~m}$.
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Question 1051 Mark
Write the two physical quantities whose dimensions are same.
Answer
Work and torque have the same dimension $\left[\mathrm{ML}^2 \mathrm{~T}^{-2}\right]$.
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Question 1061 Mark
A physical quantity $\text{X}=\frac{\text{a}^2\text{b}^{\frac{-3}{2}}}{\text{c}^4}$ A student says that the relative error in $2\frac{\Delta\text{a}}{\text{a}}-\frac{3}{2}\frac{\Delta\text{b}}{\text{b}}-4\frac{\Delta\text{c}}{\text{c}}.$ Do you agree with the student? If not, what is the relative error in X?
Answer
Errors are always additive. Therefore, the relative error in: $\text{X}=2\frac{\Delta\text{a}}{\text{a}}-\frac{3}{2}\frac{\Delta\text{b}}{\text{b}}-4\frac{\Delta\text{c}}{\text{c}}$
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Question 1071 Mark
Name some physical quantities which are dimensionless.
Answer
Solid angle, relative density, strain, Reynold's number and Poisson's ratio.
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Question 1081 Mark
The pairs of physical quantities that have the same dimensions are:
  1. Reynolds number and coefficient of friction.
  2. Latent heat and gravitational potential.
  3. Curie and frequency of light wave.
  4. Planck's constant and torque.
Answer
  1. Reynolds number and coefficient of friction.
  2. Latent heat and gravitational potential.
  3. Curie and frequency of light wave.
Explanation:
  1. Reynolds number and coefficient of friction, both are dimensionless.
  2. $\text{L}=\frac{\text{Q}}{\text{m}}=\frac{\text{ML}^2\text{T}^{-2}}{\text{M}}=[\text{L}^{2}\text{T}^{-2}]$
Gravitational Potential $=\frac{​​\text{W}}{\text{m}}=\frac{\text{ML}^{2}\text{T}^{-2}}{\text{M}}=[\text{L}^2\text{T}^{-2}]$
  1. $1$ curie $=3.7\times10^{10}$ disintegrations$/$ sec $=$
$\text{T}^{-1}$= Frequency $=\text{T}^{-1}$
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Question 1101 Mark
The unit of length convenient on the atomic scale is known as an angstrom and is denoted by $\mathring{\text{A}}:1\mathring{\text{A}}=10^{-10}\text{m}.$
The size of a hydrogen atom is about $0.5\mathring{\text{A}}.$ What is the total atomic volume in m3 of a mole of hydrogen atoms?
Answer
Radius of hydrogen atom, $\mathbf{r}=0.5 \mathring{\text{A}}=0.5 \times 10-10 \mathrm{~m}$ Volume of hydrogen atom $=4 / 3 \pi \mathrm{r}^3=4 / 3 \times 22 / 7 \times(0.5$ $\left.\times 10^{-10}\right)^3=0.524 \times 10^{-30} \mathrm{~m}^3 1$ mole of hydrogen contains $6.023 \times 10^{23}$ hydrogen atoms.
$\therefore$ Volume of 1 mole of hydrogen atoms $=6.023 \times 10^{23} \times 0.524 \times 10^{-30}=3.16 \times 10^{-7} \mathrm{~m}^3$
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Question 1111 Mark
Which of these is largest : astronomical unit, light year and par sec?
Answer
Par sec is larger than light year which in turn is larger than an astronomical unit.
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Question 1141 Mark
Express an acceleration of $10m/ s^2$ in $km/ h^2$.
Answer
Acceleration$=\frac{10\text{m}}{(1\text{s)}^2}=\frac{10\times10^{-3}}{\Big[\frac{1}{60\times60}\text{h}\Big]^2}$ $=(3600)^2\times10^{-2}\text{km}/\text{ h}^2$ $=1.29\times10^5\text{km}/\text{ h}^2$
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Question 1161 Mark
State the number of significant figures in the following: 6.320 J
Answer
4 Explanation: The given quantity is 6.320 J. For a number with decimals, the trailing zeroes are significant. Hence, all four digits appearing in the given quantity are significant figures.
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Question 1171 Mark
If $x = a + bt + ct^2$ where x is in metre and t in second, then what is the unit of e?
Answer
According to the principle of dimensions. $[\text{ct}^20]=[\text{L}]\text{ or }[\text{c}]=[\text{LT}^{-2}]$ So, the units of c is $ms^{-2}$
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Question 1181 Mark
Name two pairs of physical quantities whose dimensions are same.
Answer
Stress and Young's modulus.
Work and Energy.
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Question 1191 Mark
How many unit systems are there?
Answer
Unit systems are:
  1. $\text{FPS}$ system.
  2. $\text{MKS}$ system.
  3. $\text{CGS}$ system.
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Question 1201 Mark
The mass of a body is measured by two persons is 10.2kg and 10.23kg. Which one is more accurate and why?
Answer
The value m = 10.23kg is more accurate, being correct upto $2^{nd}$ place of decimal.
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Question 1211 Mark
A LASER is a source of very intense, monochromatic, and unidirectional beam of light. These properties of a laser light can be exploited to measure long distances. The distance of the Moon from the Earth has been already determined very precisely using a laser as a source of light. A laser light beamed at the Moon takes 2.56s to return after reflection at the Moon’s surface. How much is the radius of the lunar orbit around the Earth?
Answer
Time taken by the laser beam to return to Earth after reflection from the Moon $=2.56 \mathrm{~s}$ Speed of light $=3 \times 10^8 \mathrm{~m} / \mathrm{s}$ Time taken by the laser beam to reach Moon $=1 / 2 \times 2.56=1.28$ s Radius of the lunar orbit = Distance between the Earth and the Moon $=1.28 \times 3 \times 10^8=3.84 \times 10^8 \mathrm{~m}=3.84 \times 10^5 \mathrm{~km}$
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Question 1221 Mark
Is Avogadro's number a dimensionless quantity?
Answer
No, it has dimensions. In fact its dimensional formula is $[mol^{‑1}]$.
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Question 1241 Mark
Do A and A.U. stand for same length?
Answer
No, $1\mathring{\text{A}}=10^{-10}\text{m}$ $1\text{ A.U}=1.496\times10^{11}\text{m}$
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Question 1251 Mark
Determine $\pi$ with due regard to significant figures. $[\text{Given }\pi=3.14]$
Answer
$\pi= 3.14 \times 3.14 = 9.8596 = 9.86$
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Question 1261 Mark
Calculate the length of the arc of a circle of radius 31.0cm which subtends an angle of $\frac{\pi}{6}$ at the centre.
Answer
$\text{Angle}=\frac{\text{length of arc}}{\text{radius of arc}}$ $\frac{\pi}{6}=\frac{\text{x}}{31}$ $\text{x}=\frac{31\times\pi}{6}=\frac{31\times3.14}{6}=16.22\text{cm}.$
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Question 1271 Mark
Write the number of significant figures in each of the following measurements:
  1. $1.67 \times 10^{-27}kg.$
  2. $0.270\ cm.$
Answer
  1. Three
  2. Three
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Question 1281 Mark
Is Avogadro's number a dimensionless quantity.
Answer
No, it has dimensions. In fact, its dimensional formula I $[mol^{-1}]$.
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Question 1291 Mark
Define one Barn. How it is related with metre?
Answer
One Barn is a small unit of area used to measure area of nuclear cross-section. $\therefore1\text{ barn}=10^{-28}\text{m}^2$
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Question 1311 Mark
Write the dimensional formula of the following physical quantities:
  1. Stress.
  2. Coefficient of viscosity.
Answer
  1. Dimensional formula for stress $= ML^{-1}T^{-2}$
  2. Dimensional formula of coefficient of viscosity $= ML^{-1}T^{-1}$
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Question 1321 Mark
If all measurements in an experiment are taken upto same number of significant figures, then which measurement is responsible for maximum error?
Answer
The maximum error will be due to:
  1. Measurement which is least accurate.
  2. Measurement of the quantity which has maximum power in the formula.
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Question 1331 Mark
A jeweller put a diamond weighing 5.42g in a box weighing 1.2kg. Find the total weight of the box and the diamond to correct number of significant figures.
Answer
Weight of diamond = 5.42g = 0.00542kg Total weight = 1.2 + 0.00542 = 1.20542kg = 1.2kg
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MCQ 1341 Mark
If $3.8 \times 10^{-6}$ is added to $4.2 \times 10^{-5}$ giving due regard to significant figures, then the result will be:
  • A
    $4.58 \times 10^{-5}$
  • ✓
    $4.6 \times 10^{-5}$
  • C
    $45 \times 10^{-5}$
  • D
    None of these.
Answer
Correct option: B.
$4.6 \times 10^{-5}$
By adding $3.8 \times 10^{-6}$ and $42 \times 10^{-6}$, We get: $=45.8 \times 10^{-6}=4.58 \times 10^{-5}$ As least number of significant figures in given values are 2 , so we round off the result to $4.6 \times 10^{-5}$.
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Question 1351 Mark
If $x = a + bt + ct^2$, where x is in metres and t in second, what is the dimensional formula of c.
Answer
$[M^0L^1T^{-2}]$
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Question 1361 Mark
Percentage error in the measurement of height and radius of a cylinder are X and Y respectively. Find percentage error in the measurement of its volume. Which of the measurement height or radius need more attention?
Answer
Height of cylinder = X, radius of cylinder = Y, Volume of cylinder $\text{V}=\pi\text{Y}^2\text{X}$ Percentage error in measurement of volume: $\frac{\Delta\text{V}}{\text{V}}\times100=\pm\Big(2\frac{\Delta\text{Y}}{\text{Y}}+\frac{\Delta\text{X}}{\text{ X}}\Big)\times100$ Hence, radius needs more attention because any error in its measurement is multiplied two times.
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Question 1371 Mark
Name two physical quantities whose dimensions are same.
Answer
Stress and Young's modulus or Work and Energy have same dimension.
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Question 1381 Mark
When white light travels through glass the refractive: index $\mu=\Big(\frac{\text{Velocity of light in air}}{\text{Velocity of light in glass}}\Big)$ is found to vary with wavelength as $\mu=\text{A}+\frac{\text{B}}{\lambda^2}$ where A and B are constants. Using the principle of homogeneity of dimensions, determine the SI unit in which A and B must be expressed.
Answer
A is a constant and have no unit and SI unit of B is $m^2$.
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Question 1391 Mark
Which is a bigger unit-light year or parsec?
Answer
Parsec is bigger unit than light year (1 parsec = 3.26 light year).
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Question 1401 Mark
Give an example of: A physical quantity which has a unit but no dimensions.
Answer
Solid angle $\Omega=\frac{\text{A}}{\text{r}^2}$ steradian and a plane angle $\theta=\frac{\text{L}}{\text{r}}$ radian. Both are dimensionless but have units.
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Question 1411 Mark
What is the difference between 4.0 and 4.000?
Answer
4.0 has two significant figures whereas 4.000 has four significant figures.
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Question 1421 Mark
The period of oscillation of a simple pendulum is $\text{T}=2\pi\sqrt{\frac{\text{L}}{\text{g}}}.$ Measured value of L is 20cm known to 1mm accuracy and time for 100 oscillations of the pendulum is found to be 90s using a wrist watch of 1s resolution. What is the accuracy in the determination of g?OR
The length, breadth and thickness of a rectangular sheet of metal are 4.234m, 1.005m and 2.01cm respectively. Find the area and volume of the sheet to correct significant figures.
Answer
$\text{T}=2\pi\sqrt{\frac{\text{L}}{\text{g}}},$ Squaring both sides and rearranging for G, We have $\text{g}=\frac{4\pi^2\text{L}}{\text{T}^2}$ $\therefore\frac{\Delta\text{g}}{\text{g}}=\frac{\Delta\text{L}}{\text{L}}+\frac{2\Delta\text{T}}{\text{T}}$ $\Delta\text{L}=1\text{mm}=0.1\text{cm},$ To calculate $\frac{\Delta\text{T}}{\text{T}}$ $\text{t}=\text{nt}$ $\therefore\frac{\Delta\text{T}}{\text{T}}=\frac{\Delta\text{t}}{\text{t}}$ Putting, this value $\therefore\frac{\Delta\text{g}}{\text{g}}=\frac{\Delta\text{L}}{\text{L}}+\frac{2\Delta\text{t}}{\text{t}}$ $=\frac{0.1}{20}+2\frac{1}{90}=0.027=0.03$ Hence accurcy is 3%.OR
$\mathrm{L}=4.234 \mathrm{~m}, \mathrm{~B}=1.005 \mathrm{~m}, \mathrm{~d}=2.01 \mathrm{~cm}=2.01 \times 10^{-2} \mathrm{~m}$ Area of metal sheet $=\mathrm{L} \times \mathrm{B}=4.234 \times 1.005=4.25517 \mathrm{~m}^2$. Since both length and breadth have four significant figure area of metal sheet is given by $4.255 \mathrm{~m}^2$. Volume $=$ area $<$ thickness $=0.0855 \mathrm{~m}^3$
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Question 1431 Mark
Calculate the length of the arc of a circle of radius 31.0cm which subtends an angle of at the centre.
Answer
Hence, length of the arc = ?Radius $31.0\text{cm},\theta=\frac{\pi}{6}$
From length of the arc of a circle $\text{l}=\text{r}\theta$
$=31.0\times\frac{\pi}{6}$
$=16.2\text{cm}$
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Question 1441 Mark
State the number of significant figures in the following: $0.007m^2$
Answer
1 Explanation: The given quantity is $0.007m^2$. If the number is less than one, then all zeros on the right of the decimal point (but left to the first non-zero) are insignificant. This means that here, two zeros after the decimal are not significant. Hence, only 7 is a significant figure in this quantity.
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Question 1451 Mark
The time of oscillation t of a small drop of liquid under surface tension depends upon the density p, radius r and surface tension o. Show dimensionally that: $\text{t}=\sqrt{\frac{\rho\text{r}^3}{\sigma}}$
Answer
Given: $\text{t}=\sqrt{\frac{\rho\text{r}^3}{\sigma}}$ Where, $\rho=\text{density},​​\text{r}=\text{radius},$ $\sigma=\text{surface tesion}$ $\because[\rho]=[\text{ML}^{-3}],[\sigma]=[\text{MT}^{-2}],[\text{r}]=[\text{L}]$ $\therefore\text{R.H.S}=\Big[\frac{\text{M}^{1}\text{L}^{-3}\text{L}^3}{\text{M}^{1}\text{L}^0\text{T}^{-2}{}}\Big]^{\frac{1}{2}}$ $\Big[\frac{1}{\text{T}^{-2}}\Big]^{\frac{1}{2}}=\text{T}^{2\times\frac{1}{2}}=\text{T}$ L.H.S. = time of oscillation t of a small drop of liquid = T L.H.S. = R.H.S.
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Question 1461 Mark
A screw gauge has a pitch of 1.0mm and 200 division on the circular scale. Is is possible to increase the accuracy of the screw gauge by increasing the number of divisions on the circular scale?
Answer
No.
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Question 1471 Mark
Let us consider an equation
$
\frac{1}{2} m v^2=m g h
$
where $m$ is the mass of the body, $v$ its velocity. $g$ is the acceleration due to gravity and $h$ is the helght. Check whether this equation is dimensionally correct.
Answer
The dimensions of LHS are
$
\begin{array}{c}
{[ M ]\left[ L T ^{-1}\right]^2=[ M ]\left[ L ^2 T ^{-2}\right]} \\
=\left[ M L ^2 T ^{-2}\right]
\end{array}
$
The dimensions of RHS are
$
\begin{aligned}
{[ M ]\left[ L T ^{-2}\right][ L ] } & =[ M ]\left[ L ^2 T ^{-2}\right] \\
& =\left[ M L ^2 T ^{-2}\right]
\end{aligned}
$
The dimensions of LHS and RHS are the same and hence the equation is dimensionally correct.
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Question 1481 Mark
5.74 g of a substance occupies $1.2 cm ^3$. Express its density by keeping the significant figures in view.
Answer
There are 3 significant figures in the measured mass whereas there are only 2 significant figures in the measured volume. Hence the density should be expressed to only 2 significant figures.
$
\begin{aligned}
\text { Density } & =\frac{5.74}{1.2} g cm ^{-3} \\
& =4.8 g cm ^{-3} .
\end{aligned}
$
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Question 1491 Mark
Each side of a cube is measured to be 7.203 m. What are the total surface area and the volume of the cube to appropriate significant figures?
Answer
The number of significant figures in the measured length is 4 . The calculated area and the volume should therefore be rounded off to 4 significant figures.
$
\begin{aligned}
\text { Surface area of the cube } & =6(7.203)^2 m ^2 \\
& =311.299254 m ^2 \\
& =311.3 m ^2 \\
& =(7.203)^3 m ^3 \\
& =373.714754 m ^3 \\
& =373.7 m ^3
\end{aligned}
$
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1 Marks Question - Page 3 - Physics STD 11 Science Questions - Vidyadip