WBCHSE Class 11 Physics Measurement And Dimension Of Physical Quantity Multiple Choice Questions

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

  1. X ∝  YZ
  2. X ∝ YZ²
  3. X ∝ Y²Z
  4. X ∝ Y/Z

Answer: 2. X ∝ YZ²

Question 2. Steradian is the unit of

  1. Angle
  2. Solid angle
  3. Arc of a circle
  4. Circumference

Answer: 2. Solid angle

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

  1. Current
  2. Force
  3. Electromotive force
  4. Energy

Answer: 3. Electromotive force

Question 4. The dimensional formula of potential difference is

  1. ML2T-3A-1
  2. MLT-3A-1
  3. ML3T-3A
  4. ML2T-3A-2

Answer: 1. ML2T-3A-1

Question 5. Which of the following is dimensionally correct?

  1. Pressure = energy per unit volume
  2. Pressure = energy per unit area
  3. Pressure = force per unit length
  4. Pressure = force per unit volume

Answer: 1. Pressure = energy per unit volume

Question 6. The unit of specific conductivity is

  1. Ω • cm-1
  2. Ω-1 • cm-1
  3. Ω • cm-2
  4. 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

  1. ML2T-2
  2. ML2T-1
  3. MLT-2
  4. MLT-1

Answer: 2. ML2T-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?

  1. \(\frac{v^2 r}{g}\)
  2. \(\frac{v^2}{r g}\)
  3. \(\frac{v^2 g}{r}\)
  4. \(v^2 r g\)

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.

  1. FL-1T2
  2. FL-1T-1
  3. FLT-2
  4. F-1L-1

Answer: 1. FL-1T2

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 = kmxlygz where,

  1. x = 1, y = 1/2, z = 1
  2. x = 0, y =1/2 z = 1
  3. x = 1, y = z = 1/2
  4. 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

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

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

  1. x and q have the same unit
  2. x and p have the same unit
  3. t and q have the same unit
  4. 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

  1. x,  and λ have the same unit
  2. x and λ have the same unit, but the unit of A is different
  3. c and \(\frac{2\pi}{\lambda}\) have the same unit
  4. (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

  1. M0LT
  2. M0L-1T0
  3. M0L0T-1
  4. M0LT-1

Answer: 3. M0L0T-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

  1. 75%
  2. 100%
  3. 125%
  4. 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

  1. 12%
  2. 8%
  3. 10%
  4. 2%

Answer: 2. 8%

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

  1. Every measurement by any measuring instrument has some errors
  2. Every calculated physical quantity based on measured values has some error
  3. A measurement can have more accuracy but less precision and vice versa
  4. 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. 1.2 mm
  2. 1.25 mm
  3. 2.20 mm
  4. 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

  1. 0.02 mm
  2. 0.05 mm
  3. 0.1mm
  4. 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. 1
  2. 2
  3. 3
  4. 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 MaLbT-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

  1. (αa-βb+γc)%
  2. (αa+ βb + γc)%
  3. (αa +βb-γc)%
  4. (αa-βb-γc)%

Answer: 2. (αa+ βb + γc)%

Question 22. What is the number of significant figures in (3.10 + 4.60) x 107?

  1. 5
  2. 3
  3. 4
  4. 7

Answer: 2. 3

Question 23. The sum of 6.75 x 103 cm and 4.52 x 102 cm, keeping the significant digits only, is

  1. 7.202 x 103 cm
  2. 72.0 x 102 cm
  3. 0.72 x 104 cm
  4. 7.20 x 102 cm

Answer: 2. 72.0 x 102 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.

  1. 4.4457
  2. 4.45
  3. 4.446
  4. 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

  1. Linear impulse
  2. Angular impulse
  3. Linear momentum
  4. Angular momentum

Answer:

2. Angular impulse

4. Angular momentum

Question 26. Choose the correct statements:

  1. If a physical equation is dimensionally correct, it always expresses the correct relation among the quantities involved.
  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.
  4. 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,

  1. [ω] = T-1
  2. [a] = L
  3. [θ] = 1
  4. [k] = L-1

Answer:

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

  1. The force exerted per unit area
  2. Energy density
  3. Change in momentum per unit area per second
  4. Momentum per unit volume

Answer:

  1. The force exerted per unit area
  2. Energy density
  3. Change in momentum per unit area per second
  4. 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?

  1. (P-Q)/R
  2. PQ-R
  3. PQ/R
  4. (R+Q)/P

Answer:

1. (P-Q)/R

4. (R+Q)/P

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