## Unit 1 Physical World And Measurement Chapter 1 Measurement And Dimension Of Physical Quantity Multiple Choice Questions

**Question 1. X, Y, and Z are three physical quantities having units g · cm² · s ^{-5}, g · s^{-1}, and cm · s^{-2}. Relationship between X, Y, and Z can be represented by**

- X ∝ YZ
- X ∝ YZ²
- X ∝ Y²Z
- X ∝ Y/Z

**Answer:** 2. X ∝ YZ²

**Question 2. Steradian is the unit of**

- Angle
- Solid angle
- Arc of a circle
- Circumference

**Answer:** 2. Solid angle

**Question 3. The dimension of electric potential is the same as that of**

- Current
- Force
- Electromotive force
- Energy

**Answer:** 3. Electromotive force

**Question 4. The dimensional formula of potential difference is**

- ML
^{2}T^{-3}A^{-1} - MLT
^{-3}A^{-1} - ML
^{3}T^{-3}A - ML
^{2}T^{-3}A^{-2}

**Answer:** 1. ML^{2}T^{-3}A^{-1}

**Question 5. Which of the following is dimensionally correct?**

- Pressure = energy per unit volume
- Pressure = energy per unit area
- Pressure = force per unit length
- Pressure = force per unit volume

**Answer:** 1. Pressure = energy per unit volume

**Question 6. The unit of specific conductivity is**

- Ω • cm
^{-1} - Ω
^{-1}• cm^{-1} - Ω • cm
^{-2} - Ω
^{-1}• cm

**Answer:** 2. Ω^{-1} • cm^{-1}

**Question 7. As per quantum theory, the energy E of a photon is related to its frequency v as E = hv, where hv = Planck’s constant. Then, the dimension of h would be**

- ML
^{2}T^{-2} - ML
^{2}T^{-1} - MLT
^{-2} - MLT
^{-1}

**Answer:** 2. ML^{2}T^{-1}

**Question 8. Which of the following quantities is dimensionless, if v = speed, r = radius of a circular path, and g = acceleration due to gravity?**

- \(\frac{v^2 r}{g}\)
- \(\frac{v^2}{r g}\)
- \(\frac{v^2 g}{r}\)
- \(v^2 r g\)

**Answer:** 2. \(\frac{v^2}{r g}\)

**Question 9. Considering force (F), length (L), and time (T) to be fundamental physical quantities, find the dimension of mass.**

- FL
^{-1}T^{2} - FL
^{-1}T^{-1} - FLT
^{-2} - F
^{-1}L^{-1}T²

**Answer:** 1. FL^{-1}T^{2}

**Question 10. The time period of a pendulum (T), its length (l), the mass of its bob (m), and acceleration due to gravity (g) are related as T = km ^{x}l^{y}g^{z} where,**

- x = 1, y = 1/2, z = 1
- x = 0, y =1/2 z = 1
- x = 1, y = z = 1/2
- 0, y = 1/2 z = -1/2

**Answer:** 4. 0, y = 1/2 z = -1/2

**Question 11. The equation of the state of a gas is given by \(\left(p+\frac{a}{V^3}\right)\left(V-b^2\right)=c T\), where p, V, and T are pressure, volume and temperature respectively and a, b, c are constants. The dimensions of a and b are respectively**

- \(\mathrm{ML}^8 \mathrm{~T}^{-2} and \mathrm{L}^{3 / 2}\)
- \(\mathrm{ML}^5 \mathrm{~T}^{-2} and \mathrm{L}^3\)
- \(\mathrm{ML}^5 \mathrm{~T}^{-2} and \mathrm{L}^6\)
- \(\mathrm{ML}^6 \mathrm{~T}^{-2} and \mathrm{L}^{3 / 2}\)

**Answer:** 1. \(\mathrm{ML}^8 \mathrm{~T}^{-2} and \mathrm{L}^{3 / 2}\)

**Question 12. The unit of t is s and that of x is m in the expression, y = Acos(\(\frac{t}{p}\) – qx). Then**

- x and q have the same unit
- x and p have the same unit
- t and q have the same unit
- t and p have the same unit

**Answer:** 4. t and p have the same unit

**Question 13. The unit of both x and y is m in the expression y = \(A \sin \left[\frac{2 \pi}{\lambda}(c t-x)\right]\). Then**

- x, and λ have the same unit
- x and λ have the same unit, but the unit of A is different
- c and \(\frac{2\pi}{\lambda}\) have the same unit
- (ct-x) and \(\frac{2\pi}{\lambda}\) have the same unit

**Answer:** 1. x, and λ have the same unit

**Question 14. The dimension of ω in the expression y = Asin(ωt- kx) is**

- M
^{0}LT - M
^{0}L^{-1}T^{0} - M
^{0}L^{0}T^{-1} - M
^{0}LT^{-1}

**Answer:** 3. M^{0}L^{0}T^{-1}

**Question 15. If the error in the measurement of the momentum of a particle is 50% then the error in the measurement of kinetic energy is**

- 75%
- 100%
- 125%
- 200%

**Answer:** 2. 100%

**Question 16. Percentage errors in the measurement of mass and speed are 2% and 3% respectively. The error in the estimation of kinetic energy obtained by measuring mass and speed will be**

- 12%
- 8%
- 10%
- 2%

**Answer:** 2. 8%

**Question 17. Choose the incorrect statement out of the following.**

- Every measurement by any measuring instrument has some errors
- Every calculated physical quantity based on measured values has some error
- A measurement can have more accuracy but less precision and vice versa
- The percentage error is different from the relative error

**Answer:** 4. The percentage error is different from the relative error

**Question 18. A screw gauge has a pitch of 0.5 mm and has 50 divisions on its circular scale. Its linear and circular scale readings are, respectively, 2 mm and 2 s when the diameter of a sphere is measured by the gauge. The result of this measurement is**

- 1.2 mm
- 1.25 mm
- 2.20 mm
- 2.25 mm

**Answer:** 4. 2.25 mm

**Question 19. The smallest main scale division of a vernier caliper = 1 mm. Here, 20 vernier divisions =16 main scale divisions. The vernier constant is**

- 0.02 mm
- 0.05 mm
- 0.1mm
- 0.2 mm

**Answer:** 4. 0.2 mm

**Question 20. The measured values of mass, radius and length of a wire are, respectively, (0.3 ± 0.003) g, (0.5 ± 0.005) mm, and (6 ± 0.06) cm. The maximum percentage error in the computed value of the density of the material of the wire would be**

- 1
- 2
- 3
- 4

**Hint: Fractional errors :** \(\frac{\Delta m}{m}=\frac{0.003}{0.3}=\frac{1}{100}\);

Similarly, \(\frac{\Delta r}{r}=\frac{\Delta l}{l}=\frac{1}{100}\)

Density \((D)=\frac{m}{\pi r^2 l}\);

So, \(\frac{\Delta D}{D}=\frac{\Delta m}{m}+2 \frac{\Delta r}{r}+\frac{\Delta l}{l}=\frac{1}{100}+\frac{2}{100}+\frac{1}{100}=\frac{4}{100}=4 \%\)

**Answer:** 4. 4

**Question 21. The dimension of a quantity is M ^{a}L^{b}T^{-c}. If the measurements of mass, length, and time involve errors of α%, β%, and γ%, respectively, then the error in the measurement of the given quantity is**

- (αa-βb+γc)%
- (αa+ βb + γc)%
- (αa +βb-γc)%
- (αa-βb-γc)%

**Answer:** 2. (αa+ βb + γc)%

**Question 22. What is the number of significant figures in (3.10 + 4.60) x 10 ^{7}?**

- 5
- 3
- 4
- 7

**Answer:** 2. 3

**Question 23. The sum of 6.75 x 10 ^{3} cm and 4.52 x 10^{2} cm, keeping the significant digits only, is**

- 7.202 x 10
^{3}cm - 72.0 x 10
^{2}cm - 0.72 x 10
^{4}cm - 7.20 x 10
^{2}cm

**Answer:** 2. 72.0 x 10^{2 }cm

**Question 24. A rectangle has a length = 4.234 m and breadth = 1.05 m. What is its area in m²? Keep the significant digits only.**

- 4.4457
- 4.45
- 4.446
- 4.44

**Answer:** 2. 4.45

**In these type of questions, more than one option are correct.**

**Question 25. Photon is the quantum of radiation with energy E = hv where v is the frequency and h is Planck’s constant. The dimension of h is the same as that of**

- Linear impulse
- Angular impulse
- Linear momentum
- Angular momentum

**Answer:**

2. Angular impulse

4. Angular momentum

**Question 26. Choose the correct statements:**

- If a physical equation is dimensionally correct, it always expresses the correct relation among the quantities involved.
- Even if a physical equation is dimensionally correct, it may not express the correct relation among the quantities involved.
- If a physical equation is dimensionally incorrect, cannot express the correct relation among the quantities involved.
- Even if a physical equation is dimensionally incorrect, it may express the correct relation among the quantities involved.

**Answer:**

2. Even if a physical equation is dimensionally correct, it may not express the correct relation among the quantities involved

3. If a physical equation is dimensionally incorrect, cannot express the correct relation among the quantities involved.

**Question 27. A wave progresses along the x-axis with time t. The instantaneous displacement from the mean position is given by. y = asin[(ωt- kx) + θ]. Then, the dimensions are,**

- [ω] = T
^{-1} - [a] = L
- [θ] = 1
- [k] = L
^{-1}

**Answer:**

**Question 28. The dimension of pressure is equal to that of**

- The force exerted per unit area
- Energy density
- Change in momentum per unit area per second
- Momentum per unit volume

**Answer:**

- The force exerted per unit area
- Energy density
- Change in momentum per unit area per second
- Momentum per unit volume

**Question 29. If P, Q, and R are physical quantities having different dimensions, which of the following can never be a meaningful quantity?**

- (P-Q)/R
- PQ-R
- PQ/R
- (R+Q)/P

**Answer:**

1. (P-Q)/R

4. (R+Q)/P