Grade 11 Physics Units Quiz | Concept of Maths Ranchi

Question 1

1. A hypothetical physical quantity $X$ is defined by the relation $X = \frac{a^2 b}{c \sqrt{d}}$. If the percentage errors in the measurement of $a, b, c$ and $d$ are $1\%$, $2\%$, $3\%$ and $4\%$ respectively, what is the maximum possible percentage error in the calculation of $X$?

A) $6\%$

B) $8\%$

C) $9\%$

D) $12\%$

Answer

Correct Answer: C

Solution: The relative error propagation formula for $X$ is given by: $$ \frac{\Delta X}{X} = 2\frac{\Delta a}{a} + \frac{\Delta b}{b} + \frac{\Delta c}{c} + \frac{1}{2}\frac{\Delta d}{d} $$ Substituting the given percentage parameters: $$\text{Percentage Error} = (2 \times 1\%) + (1 \times 2\%) + (1 \times 3\%) + \left(\frac{1}{2} \times 4\%\right) = 2 + 2 + 3 + 2 = 9\%.$$

Question 2

2. In a new system of units, the unit of Mass is $10\text{ kg}$, the unit of Length is $100\text{ m}$, and the unit of Time is $1\text{ minute}$. What is the magnitude of $1\text{ Newton}$ in this new system?

A) $0.36\text{ units}$

B) $3.6\text{ units}$

C) $36\text{ units}$

D) $360\text{ units}$

Answer

Correct Answer: B

Solution: Dimensional formula of Force is $[M^1 L^1 T^{-2}]$. Using the relation $n_1 u_1 = n_2 u_2$: $$ 1 \cdot [1\text{kg} \cdot 1\text{m} \cdot (1\text{s})^{-2}] = n_2 \cdot [10\text{kg} \cdot 100\text{m} \cdot (60\text{s})^{-2}] $$ $$ n_2 = 1 \times \left(\frac{1}{10}\right) \times \left(\frac{1}{100}\right) \times \left(\frac{1}{60}\right)^{-2} = \frac{1}{1000} \times 3600 = 3.6\text{ units.} $$

Question 3

3. The Van der Waals equation for a real gas is given by $\left(P + \frac{a}{V^2}\right)(V - b) = nRT$. What are the dimensional components of the constant $a$?

Question 4

4. A scientist measures the diameter of a thin wire using a screw gauge of least count $0.001\text{ cm}$. The successive readings are $0.052\text{ cm}$, $0.053\text{ cm}$, and $0.051\text{ cm}$. The mean absolute error in these readings evaluates to:

A) $0.052\text{ cm}$

B) $0.001\text{ cm}$

C) $0.002\text{ cm}$

D) $0.00067\text{ cm}$

Answer

Correct Answer: D

Solution: Arithmetic Mean value $\bar{x} = \frac{0.052+0.053+0.051}{3} = 0.052\text{ cm}$. Individual Absolute Errors calculations: $|\Delta x_1| = |0.052-0.052|=0\text{ cm}$ $|\Delta x_2| = |0.053-0.052|=0.001\text{ cm}$ $|\Delta x_3| = |0.051-0.052|=0.001\text{ cm}$ $$\text{Mean Absolute Error} = \frac{0 + 0.001 + 0.001}{3} = \frac{0.002}{3} \approx 0.00067\text{ cm}.$$

Question 5

5. If Planck's constant ($h$), the speed of light in vacuum ($c$), and Newton's gravitational constant ($G$) are taken as foundational base fundamental units, which of the following expressions correctly represents the dimensions of Length?

A) $\sqrt{\frac{hG}{c^5}}$

B) $\frac{hG}{c^{3/2}}$

C) $\sqrt{\frac{hG}{c^3}}$

D) $h^{1/2} G^{1/2} c^{5/2}$

Answer

Correct Answer: C

Solution: Let $L \propto h^x c^y G^z$. Substituting standard base dimension definitions: $[L] = [ML^2 T^{-1}]^x \cdot [LT^{-1}]^y \cdot [M^{-1} L^3 T^{-2}]^z$. Equating exponents for $M, L, T$: $x - z = 0 \implies x = z$ $2x + y + 3z = 1$ $-x - y - 2z = 0$ Solving this linear system yields $x = 1/2, z = 1/2, y = -3/2$. Thus: $$L = \sqrt{\frac{hG}{c^3}}$$

Question 6

6. A Vernier calliper has $20$ divisions on the vernier scale which coincide precisely with $19$ divisions on the main scale. If each main scale division is $0.5\text{ mm}$, what is the least count of the instrument?

A) $0.05\text{ mm}$

B) $0.025\text{ mm}$

C) $0.01\text{ mm}$

D) $0.005\text{ mm}$

Answer

Correct Answer: B

Solution: Least Count ($\text{LC}$) = $1\text{ MSD} - 1\text{ VSD}$. Given that $20\text{ VSD} = 19\text{ MSD} \implies 1\text{ VSD} = \frac{19}{20}\text{ MSD}$. $$ \text{LC} = 1\text{ MSD} - \frac{19}{20}\text{ MSD} = \frac{1}{20}\text{ MSD} = \frac{0.5\text{ mm}}{20} = 0.025\text{ mm}. $$

Question 7

7. Which of the following pairs features completely different dimensional properties?

A) Density and Relative density

B) Impulse and Linear momentum

C) Planck's constant and Angular momentum

D) Work and Torque

Answer

Correct Answer: A

Solution: **Density** possesses dimensions of $[ML^{-3}T^0]$, whereas **Relative Density** is a ratio of identical quantities and is entirely dimensionless ($[M^0L^0T^0]$). All other given options consist of pairs sharing identical dimensional formats.

Question 8

8. The universal value of $G = 6.67 \times 10^{-11}\text{ Nm}^2 \text{kg}^{-2}$. What is its magnitude value in CGS units ($\text{g}^{-1} \text{cm}^3 \text{s}^{-2}$)?

A) $6.67 \times 10^{-5}$

B) $6.67 \times 10^{-13}$

C) $6.67 \times 10^{-7}$

D) $6.67 \times 10^{-8}$

Answer

Correct Answer: D

Solution: Converting basic fundamental units to CGS dimensions: $1\text{ N} = 10^5\text{ dyne}$, $1\text{ m} = 10^2\text{ cm}$, $1\text{ kg} = 10^3\text{ g}$. $$ G = 6.67 \times 10^{-11} \times \frac{(10^5\text{ dyne}) \times (10^2\text{ cm})^2}{(10^3\text{ g})^2} $$ $$ G = 6.67 \times 10^{-11} \times \frac{10^5 \times 10^4}{10^6} = 6.67 \times 10^{-11} \times 10^3 = 6.67 \times 10^{-8}\text{ CGS units.} $$

Question 9

9. The number of significant figures present within values $0.0006032$ and $6.032 \times 10^4$ are respectively:

A) $7$ and $4$

B) $4$ and $4$

C) $4$ and $5$

D) $8$ and $4$

Answer

Correct Answer: B

Solution: Based on significant criteria rules: leading zeros before non-zero numbers are placeholders and not significant. Thus, $0.0006032$ contains $4$ significant digits ('6032'). For numbers in scientific notation, exponential factors do not contribute, giving $6.032 \times 10^4$ exactly $4$ significant figures.

Question 10

10. The frequency of vibration $f$ of a stretched string depends on its length $L$, the tracking tension force $T$, and its mass per unit length $\mu$. Using structural dimensional metrics, the proportional relation resolves to:

A) $f \propto \frac{1}{L} \sqrt{\mu T}$

B) $f \propto L \sqrt{T/\mu}$

C) $f \propto \frac{1}{L} \sqrt{T/\mu}$

D) $f \propto \frac{L}{\sqrt{T\mu}}$

Answer

Correct Answer: C

Solution: Let $f = k L^a T^b \mu^c$. Substituting dimensional formulas: $[M^0 L^0 T^{-1}] = [L]^a \cdot [M^1 L^1 T^{-2}]^b \cdot [M^1 L^{-1}]^c$. System components matching breakdown: $b + c = 0 \implies c = -b$ $a + b - c = 0$ $-2b = -1 \implies b = 1/2$. This yields $b = 1/2, c = -1/2, a = -1$. Therefore: $$f \propto \frac{1}{L} \sqrt{\frac{T}{\mu}}$$

Question 11

11. A screw gauge with a pitch of $0.5\text{ mm}$ and $100$ individual divisions on its circular scale layout is tracking a plate width. If the circular scale reading points to $48$ and main scale records $2.5\text{ mm}$, what is the thickness?

A) $2.74\text{ mm}$

B) $2.98\text{ mm}$

C) $2.548\text{ mm}$

D) $3.00\text{ mm}$

Answer

Correct Answer: A

Solution: $\text{Least Count (LC)} = \frac{\text{Pitch}}{\text{Total Divisions}} = \frac{0.5\text{ mm}}{100} = 0.005\text{ mm}$. $$\text{Total Thickness Reading} = \text{Main Scale Reading} + (\text{Circular Scale Reading} \times \text{LC})$$ $$\text{Thickness} = 2.5\text{ mm} + (48 \times 0.005\text{ mm}) = 2.5 + 0.24 = 2.74\text{ mm}.$$

Question 12

12. If force ($F$), velocity ($V$), and time ($T$) are adopted as fundamental structural entities, what is the correct dimensional expression for Surface Tension?

A) $[FV^{-1}T^{-2}]$

B) $[FV^{-1}T^{-1}]$

C) $[FV^{-2}T^{-1}]$

D) $[F^2 V T^{-1}]$

Answer

Correct Answer: B

Solution: Surface Tension ($\sigma$) is defined as Force per unit length ($F/L$). Since $\text{Velocity} = \frac{\text{Length}}{\text{Time}} \implies L = V \times T$. Substituting this dimension profile yields: $$\sigma = \frac{F}{V \cdot T} = [FV^{-1}T^{-1}].$$

Question 13

13. The measured tracking percentage error for a sphere's radius is $1.5\%$. What will be the maximum percentage error calculation inside its total Volume?

A) $1.5\%$

B) $3.0\%$

C) $4.5\%$

D) $6.0\%$

Answer

Correct Answer: C

Solution: Volume of a sphere $V = \frac{4}{3}\pi r^3$. Expressing this via fractional errors gives: $\frac{\Delta V}{V} = 3 \times \left(\frac{\Delta r}{r}\right)$. $$\text{Percentage Error in Volume} = 3 \times 1.5\% = 4.5\%.$$

Question 14

14. What are the base dimensions for the solar constant (defined as incident energy received per unit surface area per unit tracking time)?

A) $[ML^2 T^{-2}]$

B) $[MT^{-2}]$

C) $[MLT^{-3}]$

D) $[MT^{-3}]$

Answer

Correct Answer: D

Solution: $$\text{Solar Constant} = \frac{\text{Energy}}{\text{Area} \times \text{Time}}$$ Substituting the corresponding dimensions: $$\text{Dimensions} = \frac{[ML^2 T^{-2}]}{[L^2] \cdot [T]} = [M^1 L^0 T^{-3}] = [MT^{-3}].$$

Question 15

15. Inside the wave layout expression $y = a \sin(\omega t - kx)$, where $t$ maps time metrics and $x$ marks dimensional distance, the structural profile parameters $\omega/k$ match the dimensions of:

A) Velocity

B) Acceleration

C) Wavelength

D) Frequency

Answer

Correct Answer: A

Solution: The trigonometric arguments inside a sine function must always remain dimensionless. $[\omega t] = [1] \implies [\omega] = [T^{-1}]$ $[kx] = [1] \implies [k] = [L^{-1}]$ Therefore, dividing these parameters yields: $$\left[\frac{\omega}{k}\right] = \frac{[T^{-1}]}{[L^{-1}]} = [LT^{-1}]\text{, which matches the dimensions of Velocity.}$$

Question 16

16. A complex physical property $P$ scales via the expression $P = \frac{A^3 B^{1/2}}{C^{-4} D^{3/2}}$. If variables $A, B, C, D$ all share identical percentage measurements error factors, which individual element contributes the absolute MINIMUM error fraction to $P$?

A) A

B) C

C) B

D) D

Answer

Correct Answer: C

Solution: Expanding the relative error equation yields: $$ \frac{\Delta P}{P} = 3\left(\frac{\Delta A}{A}\right) + 0.5\left(\frac{\Delta B}{B}\right) + 4\left(\frac{\Delta C}{C}\right) + 1.5\left(\frac{\Delta D}{D}\right) $$ The variable tracking the absolute smallest numerical power exponent multiplier (coefficient) acts as the lowest overall contributor. Here, $B$ maps an index of $0.5$, providing the minimum overall error impact.

Question 17

17. If a clock pendulum length measures $20.0\text{ cm}$ using a tracking scale of $1\text{ mm}$ accuracy, while the collection duration for $100$ cycles resolves to $90\text{ s}$ via a $1\text{ s}$ resolution watch, the net calculation error inside $g$ evaluates to:

A) $1.5\%$

B) $2.7\%$

C) $3.4\%$

D) $5.0\%$

Answer

Correct Answer: B

Solution: The acceleration due to gravity is modeled via $g = \frac{4\pi^2 L}{T^2}$, which gives the error relation: $\frac{\Delta g}{g} = \frac{\Delta L}{L} + 2\left(\frac{\Delta T}{T}\right)$. Substituting the measured properties (converting units to match): $\frac{\Delta L}{L} = \frac{0.1\text{ cm}}{20.0\text{ cm}} = 0.005$ $\frac{\Delta T}{T} = \frac{1\text{ s}}{90\text{ s}} \approx 0.0111$ $$\frac{\Delta g}{g} = 0.005 + 2(0.0111) = 0.005 + 0.0222 = 0.0272 \approx 2.7\%.$$

Question 18

18. The systemic dimensions representing expression $\frac{1}{\sqrt{\mu_0 \epsilon_0}}$ match exactly with:

A) Velocity of light

B) Impedance

C) Inductance

D) Capacitance

Answer

Correct Answer: A

Solution: From classical Maxwell electrodynamics equations, the transmission propagation speed of electro-magnetic waves inside open vacuum media is explicitly defined as $c = \frac{1}{\sqrt{\mu_0 \epsilon_0}}$. Thus, it shares identical dimensions with the velocity of light ($[L^1 T^{-1}]$).

Question 19

19. What is the correct standard SI unit representing thermal conductivity metrics?

A) $\text{J m}^{-1} \text{K}^{-1}$

B) $\text{W m K}^{-1}$

C) $\text{W m}^{-1} \text{s}^{-1}$

D) $\text{W m}^{-1} \text{K}^{-1}$

Answer

Correct Answer: D

Solution: The baseline rate equation for linear thermal heat flow is: $\frac{dQ}{dt} = KA\left(\frac{dT}{dx}\right)$. Isolating conductivity parameter $K = \left(\frac{dQ}{dt}\right) \times \left(\frac{dx}{A \cdot dT}\right)$. $$\text{Units} = (\text{Watt}) \times \frac{\text{m}}{\text{m}^2 \cdot \text{K}} = \text{W m}^{-1} \text{K}^{-1}.$$

Question 20

20. What is the fundamental dimensional configuration formula representing magnetic flux ($\Phi$)?

A) $[ML^2 T^{-2} A^{-2}]$

B) $[ML T^{-2} A^{-1}]$

C) $[ML^2 T^{-2} A^{-1}]$

D) $[ML^2 T^{-1} A^{-1}]$

Answer

Correct Answer: C

Solution: Magnetic flux matches the relation $\Phi = B \cdot A$. From the Lorentz force relation $F = qvB \implies B = \frac{F}{qv}$. $$\Phi = \frac{F \cdot A}{qv} = \frac{[MLT^{-2}] \cdot [L^2]}{[AT] \cdot [LT^{-1}]} = [ML^2 T^{-2} A^{-1}].$$

Accepted Answer

Correct Answer: A

Solution: By the dimensional principle of homogeneity, quantities with identical dimensions can only be added or subtracted together. Thus, the dimensions of $P$ must equal the dimensions of $\frac{a}{V^2}$. $$ [a] = [P][V^2] = [ML^{-1} T^{-2}] \cdot [L^3]^2 = [ML^{-1} T^{-2}][L^6] = [ML^5 T^{-2}]. $$

Grade 11 : Physics - Units (Set 3) | Concept of Maths

Grade 11 : Physics - Units (Set 3) | Concept of Maths

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4. A scientist measures the diameter of a thin wire using a screw gauge of least count $0.001\text{ cm}$. The successive readings are $0.052\text{ cm}$, $0.053\text{ cm}$, and $0.051\text{ cm}$. The mean absolute error in these readings evaluates to:

5. If Planck's constant ($h$), the speed of light in vacuum ($c$), and Newton's gravitational constant ($G$) are taken as foundational base fundamental units, which of the following expressions correctly represents the dimensions of Length?

6. A Vernier calliper has $20$ divisions on the vernier scale which coincide precisely with $19$ divisions on the main scale. If each main scale division is $0.5\text{ mm}$, what is the least count of the instrument?

7. Which of the following pairs features completely different dimensional properties?

8. The universal value of $G = 6.67 \times 10^{-11}\text{ Nm}^2 \text{kg}^{-2}$. What is its magnitude value in CGS units ($\text{g}^{-1} \text{cm}^3 \text{s}^{-2}$)?

9. The number of significant figures present within values $0.0006032$ and $6.032 \times 10^4$ are respectively:

10. The frequency of vibration $f$ of a stretched string depends on its length $L$, the tracking tension force $T$, and its mass per unit length $\mu$. Using structural dimensional metrics, the proportional relation resolves to:

11. A screw gauge with a pitch of $0.5\text{ mm}$ and $100$ individual divisions on its circular scale layout is tracking a plate width. If the circular scale reading points to $48$ and main scale records $2.5\text{ mm}$, what is the thickness?

12. If force ($F$), velocity ($V$), and time ($T$) are adopted as fundamental structural entities, what is the correct dimensional expression for Surface Tension?

13. The measured tracking percentage error for a sphere's radius is $1.5\%$. What will be the maximum percentage error calculation inside its total Volume?

14. What are the base dimensions for the solar constant (defined as incident energy received per unit surface area per unit tracking time)?

15. Inside the wave layout expression $y = a \sin(\omega t - kx)$, where $t$ maps time metrics and $x$ marks dimensional distance, the structural profile parameters $\omega/k$ match the dimensions of:

16. A complex physical property $P$ scales via the expression $P = \frac{A^3 B^{1/2}}{C^{-4} D^{3/2}}$. If variables $A, B, C, D$ all share identical percentage measurements error factors, which individual element contributes the absolute MINIMUM error fraction to $P$?

17. If a clock pendulum length measures $20.0\text{ cm}$ using a tracking scale of $1\text{ mm}$ accuracy, while the collection duration for $100$ cycles resolves to $90\text{ s}$ via a $1\text{ s}$ resolution watch, the net calculation error inside $g$ evaluates to:

18. The systemic dimensions representing expression $\frac{1}{\sqrt{\mu_0 \epsilon_0}}$ match exactly with:

19. What is the correct standard SI unit representing thermal conductivity metrics?

20. What is the fundamental dimensional configuration formula representing magnetic flux ($\Phi$)?

Grade 11 Physics Units Quiz | Concept of Maths Ranchi

1. A hypothetical physical quantity $X$ is defined by the relation $X = \frac{a^2 b}{c \sqrt{d}}$. If the percentage errors in the measurement of $a, b, c$ and $d$ are $1\%$, $2\%$, $3\%$ and $4\%$ respectively, what is the maximum possible percentage error in the calculation of $X$?

2. In a new system of units, the unit of Mass is $10\text{ kg}$, the unit of Length is $100\text{ m}$, and the unit of Time is $1\text{ minute}$. What is the magnitude of $1\text{ Newton}$ in this new system?

3. The Van der Waals equation for a real gas is given by $\left(P + \frac{a}{V^2}\right)(V - b) = nRT$. What are the dimensional components of the constant $a$?

Grade 11 : Physics - Units (Set 3) | Concept of Maths

Grade 11 : Physics - Units (Set 3) | Concept of Maths

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4. A scientist measures the diameter of a thin wire using a screw gauge of least count $0.001\text{ cm}$. The successive readings are $0.052\text{ cm}$, $0.053\text{ cm}$, and $0.051\text{ cm}$. The mean absolute error in these readings evaluates to:

5. If Planck's constant ($h$), the speed of light in vacuum ($c$), and Newton's gravitational constant ($G$) are taken as foundational base fundamental units, which of the following expressions correctly represents the dimensions of Length?

6. A Vernier calliper has $20$ divisions on the vernier scale which coincide precisely with $19$ divisions on the main scale. If each main scale division is $0.5\text{ mm}$, what is the least count of the instrument?

7. Which of the following pairs features completely different dimensional properties?

8. The universal value of $G = 6.67 \times 10^{-11}\text{ Nm}^2 \text{kg}^{-2}$. What is its magnitude value in CGS units ($\text{g}^{-1} \text{cm}^3 \text{s}^{-2}$)?

9. The number of significant figures present within values $0.0006032$ and $6.032 \times 10^4$ are respectively:

10. The frequency of vibration $f$ of a stretched string depends on its length $L$, the tracking tension force $T$, and its mass per unit length $\mu$. Using structural dimensional metrics, the proportional relation resolves to:

11. A screw gauge with a pitch of $0.5\text{ mm}$ and $100$ individual divisions on its circular scale layout is tracking a plate width. If the circular scale reading points to $48$ and main scale records $2.5\text{ mm}$, what is the thickness?

12. If force ($F$), velocity ($V$), and time ($T$) are adopted as fundamental structural entities, what is the correct dimensional expression for Surface Tension?

13. The measured tracking percentage error for a sphere's radius is $1.5\%$. What will be the maximum percentage error calculation inside its total Volume?

14. What are the base dimensions for the solar constant (defined as incident energy received per unit surface area per unit tracking time)?

15. Inside the wave layout expression $y = a \sin(\omega t - kx)$, where $t$ maps time metrics and $x$ marks dimensional distance, the structural profile parameters $\omega/k$ match the dimensions of:

16. A complex physical property $P$ scales via the expression $P = \frac{A^3 B^{1/2}}{C^{-4} D^{3/2}}$. If variables $A, B, C, D$ all share identical percentage measurements error factors, which individual element contributes the absolute MINIMUM error fraction to $P$?

17. If a clock pendulum length measures $20.0\text{ cm}$ using a tracking scale of $1\text{ mm}$ accuracy, while the collection duration for $100$ cycles resolves to $90\text{ s}$ via a $1\text{ s}$ resolution watch, the net calculation error inside $g$ evaluates to:

18. The systemic dimensions representing expression $\frac{1}{\sqrt{\mu_0 \epsilon_0}}$ match exactly with:

19. What is the correct standard SI unit representing thermal conductivity metrics?

20. What is the fundamental dimensional configuration formula representing magnetic flux ($\Phi$)?