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Units and Measurements physics ncert solutions class 11th Physics Class 11th Physics NCERT Exemplar Solutions Class 11th Chapter Two

Give an example of

(a) A physical quantity which has a unit but no dimensions.

(b) A physical quantity which has neither unit nor dimensions.

(c) A constant which has a unit.

(d) A constant which has no unit.

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1 Answer

Answered by

Payal Gupta | Contributor-Level 10

3 months ago

This is a short answer type question as classified in NCERT Exemplar

(a) Plane angle = l/r radian its si unit is radian but no dimension formula.

(b) Strain= $\frac{? L}{L} = \frac{c h a n g e i n l e n g t h}{l e n g t h}$ so no dimension

And g =9.8m/s²

(c) Gravitational constant G= 6.67 $\times 10^{- 11} N m^{2} / {k g}^{2}$

(d) Reynold’s number is a number having no dimension.

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A vessel contains 16g of hydrogen and 128g of oxygen at standard temperature and pressure. The volume of the vessel in cm³ is:

Vishal Baghel

According to question, we can write

Total moles of gas = n = n_Oxygen+ n_Oxygen= $\frac{16}{2} + \frac{128}{32} = 12 m o l e s$

Volume of gas = 12 × 22.4 litre = 268.8 litre = 2.688 × 10⁵ cm³ $\approx 27 \times 1 0^{4} c m^{3}$

Dimensional formula for thermal conductivity is (here K denotes the temperature):

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$K = \frac{(\frac{Q}{r}) Δ x}{Δ A T}$

$\begin{array}{l} \Rightarrow & \frac{({M L}^{2} T^{- 2}) (L)}{(L^{2}) (θ) (T)} \\ \Rightarrow & M^{1} L^{1 -} T^{- 3} θ^{- 1} \end{array}$

It momentum [P], area [A] and time [T] are taken as fundamental quantities, then the dimensional formula for coefficient of viscosity is:

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Viscosity = Pascal . Second

$P^{X} A^{Y} T^{Z} = [M^{1} L^{- 1} T^{- 1}]$

= ${[M^{1} L^{+ 1} T^{- 1}]}^{x} [L^{2}] y {[T^{1}]}^{z} = M^{- 1} L^{- 1} T^{- 1}$

= x = 1, x + 2y = -1, -x + z = 1

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The one division of main scale of Vernier calipers reads 1mm and 10 divisions of Vernier scale is equal to the 9 divisions on main scale, When the two jaws of the instrument touch each other, the zero of the Vernier lies to the right of zero of the main scale and its fourth division coincides with a main scale division. When a spherical bob is tightly placed between the two jaws, the zero of the Vernier scale lies in between 4.1 cm and 4.2cm and 6^th Vernier division coincides with a main scale division. The diameter of the bob will be ________× 10^-2 cm.

Payal Gupta

1 msD = 1mm

10 vsD = 9msD

1vsD = 0.9 MsD

L.C. = 1MSD – 1VSD = 1 – 0.9 = 0.1 mm

Zero error = 4LC = 0.4 mm

Reading = MSR + VSR + correction

= 4.1 cm + 6 * .01 cm + (-0.04 cm) = (4.1 + 0.06 – 0.04) cm

= 4.12 cm = 412 * 10^-² cm

Identify the pair of physical quantities which have different dimensions

Vishal Baghel

$Δ Q = m s Δ T \Rightarrow s = \frac{Δ Q}{m Δ T} \Rightarrow [s] = \frac{M L^{2} T^{- 2}}{M Q} = L^{2} T^{- 2} Q^{- 1}$

$Δ Q = m L \Rightarrow [L] = \frac{M L^{2} T^{- 2}}{M} = L^{2} T^{- 2}$

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Give an example of

(a) A physical quantity which has a unit but no dimensions.

(b) A physical quantity which has neither unit nor dimensions.

(c) A constant which has a unit.

(d) A constant which has no unit.

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Give an example of (a) A physical quantity which has a unit but no dimensions. (b) A physical quantity which has neither unit nor dimensions. (c) A constant which has a unit. (d) A constant which has no unit.

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Give an example of

(a) A physical quantity which has a unit but no dimensions.

(b) A physical quantity which has neither unit nor dimensions.

(c) A constant which has a unit.

(d) A constant which has no unit.