Grade 11 Physics Quiz: Units & Measurements (Set 5) - Concept of Maths

Question 1

In a hypothetical universe, the Planck length $l_p$, the speed of light c, and the universal gravitational constant G are taken as base units. What is the dimensional formula for 'Mass' in this system?

Accepted Answer

C) $[l_p c^2 G^{-1}]$ is incorrect; the correct derivation is $[l_p c^2 G^{-1}]$

Answer

A) $[l_p c^2 G^{-1}]$

Answer

B) $[l_p c G^{-1/2}]$

Answer

D) $[l_p c^2 G^{-1}]$ actually results in Mass dimensions if derived from $l_p = \sqrt{\frac{hG}{c^3}}$. Let us use $M = \frac{l_p c^2}{G}$.

Question 2

A research vessel measures the density of a deep-sea mineral sample. The mass is recorded as $m = (250 \pm 0.5) \g$ and the volume as $V = (50 \pm 0.2) \cm^3$. What is the maximum percentage error in the calculated density?

Accepted Answer

B) 0.6\%

Answer

A) 0.2\%

Answer

C) 0.7\%

Answer

D) 1.0\%

Question 3

The Stefan-Boltzmann law states that the energy radiated per unit area per unit time is $E = \sigma T^4$. What are the SI base units of the Stefan-Boltzmann constant \sigma?

Accepted Answer

D) $[kg \cdot s^{-3} \cdot K^{-4}]$

Answer

A) $[kg \cdot s^{-2} \cdot K^{-4}]$

Answer

B) $[kg \cdot m^2 \cdot s^{-3} \cdot K^{-4}]$

Answer

C) $[kg \cdot m \cdot s^{-3} \cdot K^{-4}]$

Question 4

If the velocity of light c, the acceleration due to gravity g, and the atmospheric pressure P are the fundamental quantities, what is the dimension of 'Length'?

Accepted Answer

A) $[c^2 g^{-1}]$

Answer

B) $[c g^{-1}]$

Answer

C) [P g / c]

Answer

D) $[c^2 / P]$

Question 5

A physical quantity X is defined as $X = \frac{h}{e^2} \sqrt{\frac{\mu_0}{\epsilon_0}}$, where h is Planck's constant, e is elementary charge, $\mu_0$ is permeability of vacuum, and $\epsilon_0$ is permittivity of vacuum. What is the dimension of X?

Accepted Answer

C) $[M^0 L^0 T^0 A^0]$ - Dimensionless

Answer

A) $[M^0 L^0 T^0 A^0]$

Answer

B) $[M L^2 T^{-3} A^{-2}]$

Answer

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

Question 6

The parallax of a heavenly body measured from two points diametrically opposite on Earth's equator is 2.0 arc minutes. If the radius of Earth is 6400 \km, find the distance of the body from the center of the Earth.

Accepted Answer

B) $2.2 \times 10^7 \km$

Answer

A) $1.1 \times 10^7 \km$

Answer

C) $1.1 \times 10^8 \km$

Answer

D) $4.4 \times 10^7 \km$

Question 7

A student measures the diameter of a steel ball using a screw gauge of least count 0.001 \cm. The main scale reading is 5 \ mm and zero of circular scale division coincides with 25 divisions above the reference level. If the screw gauge has a zero error of -0.004 \cm, the correct diameter is:

Accepted Answer

D) 0.529 \cm is correctly calculated as 0.5 + 0.025 + 0.004

Answer

A) 0.521 \cm

Answer

B) 0.525 \cm

Answer

C) 0.529 \cm

Question 8

Which of the following pairs of physical quantities have the same dimensions?

Accepted Answer

A) Magnetic flux and Electromotive force $\times$ Time

Answer

B) Energy and Torque $\times$ Angle

Answer

C) Pressure and Modulus of Elasticity

Answer

D) All of the above

Question 9

If the error in the measurement of radius of a sphere is 2\%, then the error in the determination of its volume will be:

Accepted Answer

B) 6\%

Answer

A) 4\%

Answer

C) 8\%

Answer

D) 2\%

Question 10

The dimensions of the coefficient of thermal conductivity K are:

Accepted Answer

C) $[M L T^{-3} K^{-1}]$

Answer

A) $[M L T^{-3} K^{-1}]$

Answer

B) $[M L^2 T^{-3} K^{-1}]$

Answer

D) $[M L^2 T^{-2} K^{-1}]$

Question 11

The frequency of vibration f of a mass m suspended from a spring of spring constant k is given by $f = a m^x k^y$, where a is a dimensionless constant. The values of x and y are:

Accepted Answer

A) x = -1/2, y = 1/2

Answer

B) x = 1/2, y = -1/2

Answer

C) x = 1/2, y = 1/2

Answer

D) x = -1, y = 1

Question 12

A physical quantity is represented by $Y = M^a L^b T^c$. The percentage error in measurement of M, L, T are $\alpha, \beta, \gamma$ respectively. The maximum percentage error in Y is:

Accepted Answer

B) $(|a|\alpha + |b|\beta + |c|\gamma)$

Answer

A) $(a\alpha + b\beta + c\gamma)$

Answer

C) $(a\alpha - b\beta - c\gamma)$

Answer

D) None of these

Question 13

In the relation $P = \frac{a - x^2}{bt}$, where P is pressure, x is distance, and t is time, find the dimensions of a/b.

Accepted Answer

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

Answer

A) $[ML^2T^{-3}]$

Answer

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

Answer

D) $[M^2L T^{-3}]$

Question 14

The dimensions of $\frac{1}{2} \epsilon_0 E^2$ (where $\epsilon_0$ is permittivity of free space and E is electric field) are:

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 15

Which of the following is the most precise device for measuring length?

Accepted Answer

A) An optical instrument that can measure length to within a wavelength of light (500 \ nm)

Answer

B) A screw gauge with pitch 1 \ mm and 100 divisions on the circular scale

Answer

C) A vernier caliper with 20 divisions on the sliding scale coinciding with 19 divisions on the main scale (1 \ mm)

Answer

D) A standard meter scale with 1 \ mm markings

Question 16

The velocity v of a particle depends on time t according to the equation $v = a + bt + \frac{c}{d + t}$. The dimensions of a, b, c, d are:

Accepted Answer

D) $[LT^{-1}], [LT^{-2}], [L], [T]$

Answer

A) $[L], [LT], [L^2], [T]$

Answer

B) $[LT^{-1}], [LT^{-2}], [L], [T]$

Answer

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

Question 17

If E, M, J and G denote energy, mass, angular momentum and gravitational constant respectively, the quantity $P = EJ^2 / M^5G^2$ has the dimensions of:

Accepted Answer

B) Angle

Answer

A) Length

Answer

C) Mass

Answer

D) Time

Question 18

The unit of permeability of free space $\mu_0$ is:

Accepted Answer

C) Both A and B

Answer

A) $Wb \cdot A^{-1} \cdot m^{-1}$

Answer

B) $H \cdot m^{-1}$

Answer

D) $Tesla \cdot m^2 \cdot A^{-1}$

Question 19

The number of significant figures in $0.007 \m^2$ and 6.320 \ J are respectively:

Accepted Answer

B) 1 and 4

Answer

A) 3 and 3

Answer

C) 1 and 3

Answer

D) 4 and 4

Question 20

A physical quantity P is given by $P = \frac{A^3 B^{1/2}}{C^{-4} D^{3/2}}$. Which quantity brings the maximum percentage error in P?

Accepted Answer

A) C

Answer

B) A

Answer

C) D

Answer

D) B