Question types

Units and Measurements question types

51 questions across 5 question groups — pick any mix to generate a Physics paper with step-by-step answer keys.

51
Questions
5
Question groups
5
Question types
Sample Questions

Units and Measurements questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

If P, Q, R are physical quantities, having different dimensions, which of the following combinations can never be a meaningful quantity?

  1. $\frac{(\text{P}-\text{Q})}{\text{R}}$

  2. $\text{PQ}-\text{R}$

  3. $\frac{\text{PQ}}{\text{R}}$

  4. $\frac{(\text{PR}-\text{Q}^2)}{\text{R}}$

  5. $\frac{(\text{R}+\text{Q})}{\text{P}}$

View full solution
On the basis of dimensions, decide which of the following relations for the displacement of a particle undergoing simple harmonic motion is not correct:

  1. $\text{y}=\frac{\text{a}\sin2\pi\text{t}}{\text{T}}.$

  2. $\text{y}=\text{a}\sin\text{vt}.$

  3. $\text{y}=\frac{\text{a}}{\text{T}}\sin\Big(\frac{\text{t}}{\text{a}}\Big).$

  4. $\text{y}=\text{a}\sqrt{2}\Big(\sin\frac{2\pi\text{t}}{\text{T}}-\cos\frac{2\pi\text{t}}{\text{T}}\Big).$

View full solution
Measure of two quantities along with the precision of respective measuring instrument is:

$\text{A} = 2.5\text{ms}^{-1} \pm 0.5\text{ms}^{-1}$

$\text{B} = 0.10\text{s} \pm 0.01\text{s}$

The value of A B will be,

  1. $(0.25 \pm 0.08)\text{m}.$

  2. $(0.25 \pm 0.5)\text{m}.$

  3. $(0.25 \pm 0.05)\text{m}.$

  4. $(0.25 \pm 0.135)\text{m}$

View full solution
Which of the following ratios express pressure?

  1. $\frac{\text{Force}}{\text{Area}}.$

  2. $\frac{\text{Energy}}{\text{Volume}}.$

  3. $\frac{\text{Energy}}{\text{Area}}.$

  4. $\frac{\text{Force}}{\text{Volume}}.$

View full solution
The length and breadth of a rectangular sheet are 16.2cm and 10.1cm, respectively. The area of the sheet in appropriate significant figures and error is:

  1. $164 \pm 3 \text{cm}^2$.

  2. $163.62 \pm 2.6 \text{cm}^2.$

  3. $163.6 \pm 2.6 \text{cm}^2.$

  4. $163.62 \pm 3 \text{cm}^2.$

View full solution
If velocity of light c, Planck’s constant h and gravitational contant G are taken as fundamental quantities then express mass, length and time in terms of dimensions of these quantities.
View full solution
The vernier scale of a travelling microscope has 50 divisions which coincide with 49 main scale divisions. If each main scale division is 0.5mm, calculate the minimum inaccuracy in the measurement of distance.
View full solution
Q 163 Marks Question3 Marks
In the expression P = El2 m-5 G-2, E, m, l and G denote energy, mass, angular momentum and gravitational constant, respectively. Show that P is a dimensionless quantity.
View full solution
Q 183 Marks Question3 Marks
The volume of a liquid flowing out per second of a pipe of length l and radius r is written by a student as,

$\text{v}=\frac{\pi}{8}\frac{\text{Pr}^4}{\eta\text{l}}$

where P is the pressure difference between the two ends of the pipe and $\eta$ is coefficent of viscosity of the liquid having dimensional formula ML-1 T-1.

Check whether the equation is dimensionally correct.

View full solution
Q 193 Marks Question3 Marks
Consider a sunlike star at a distance of 2 parsecs. When it is seen through a telescope with 100 magnification, what should be the angular size of the star? Sun appears to be $\Big(\frac{1}{2}\Big)^0$ from the earth. Due to atmospheric fluctuations, eye can’t resolve objects smaller than 1 arc minute.
View full solution
Q 203 Marks Question3 Marks
The displacement of a progressive wave is represented by $\text{y} = \text{A} \sin(\omega \text{t} – \text{k x} ),$ where x is distance and t is time. Write the dimensional formula of (i) $\omega$ and (ii) k.
View full solution
In an experiment to estimate the size of a molecule of oleic acid 1mL of oleic acid is dissolved in 19mL of alcohol. Then 1mL of this solution is diluted to 20mL by adding alcohol. Now 1 drop of this diluted solution is placed on water in a shallow trough. The solution spreads over the surface of water forming one molecule thick layer. Now, lycopodium powder is sprinkled evenly over the film and its diameter is measured. Knowing the volume of the drop and area of the film we can calculate the thickness of the film which will give us the size of oleic acid molecule.
Read the passage carefully and answer the following questions:
  1. Why do we dissolve oleic acid in alcohol?
  2. What is the role of lycopodium powder?
  3. What would be the volume of oleic acid in each mL of solution prepared?
  4. How will you calculate the volume of n drops of this solution of oleic acid?
  5. What will be the volume of oleic acid in one drop of this solution?
View full solution
A new system of units is proposed in which unit of mass is $\alpha\text{kg},$ unit of length $\beta$ m and unit of time $\gamma\text{ s}.$ How much will 5J measure in this new system?
View full solution
An artificial satellite is revolving around a planet of mass M and radius R, in a circular orbit of radius r. From Kepler’s Third law about the period of a satellite around a common central body, square of the period of revolution T is proportional to the cube of the radius of the orbit r. Show using dimensional analysis, that $\text{T}=\frac{\text{k}}{\text{R}}\sqrt{\frac{\text{r}^3}{\text{g}}},$ where k is a dimensionless constant and g is acceleration due to gravity.
View full solution
Mars has approximately half of the earth’s diameter. When it is closest to the earth it is at about $\frac{1}{2}$ A.U. from the earth. Calculate what size it will appear when seen through the same telescope.
View full solution

Generate a Units and Measurements paper free

Pick question groups from the list above, set marks and difficulty, and export a branded PDF with step-by-step answer keys. First 3 chapters free — no signup.

Download App