Units and Measurement

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New answer posted•a year ago

Units and Measurement Class 11th

If force (F), length (L) and time (T) are taken as the fundamental quantities. Then what will be the dimension of density:

2 Views|Posted a year ago

Asked by Alok Kumar Singh

Answered by

Alok Kumar Singh | Contributor-Level 10

a year ago

$[F] = M L T^{- 2} \Rightarrow M = F L^{- 1} T^{2}$

$[ρ] = M L^{- 3} = F L^{- 1} T^{2} L^{- 3} = F L^{- 4} T^{2}$

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New answer posted•a year ago

Units and Measurement Class 11th

Which of the following is not a dimensionless quantity?

4 Views|Posted a year ago

Asked by Vishal Baghel

Answered by

Vishal Baghel | Contributor-Level 10

a year ago

$μ_{0} = \frac{B_{0}}{H} = N A^{- 2}$

$[μ_{0}] = [M^{1} L^{1} T^{- 2} A^{- 2}]$

It is not dimensionless

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New answer posted•a year ago

Units and Measurement Class 11th

Match List II with List II

List I List II

(A) R_H(Rydberg constant) (i) kg m^-¹s^-¹

(B) h (Planck’s constant) (ii) kg m²s^-¹

(C)  $μ_{B}$ (Magnetic field energy density) (iii) m^-¹

(D)  $η$ (coefficient of viscocity (iv) kg m^-¹s^-²

5 Views|Posted a year ago

Asked by Alok Kumar Singh

Answered by

Alok Kumar Singh | Contributor-Level 10

a year ago

R_H : m^-1

h : kgm² s^-1

$μ_{B} : k g m^{- 1} s^{- 2}$

$η : k g m^{- 1} s^{- 1}$

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New answer posted•a year ago

Units and Measurement Class 11th

For $z = a^{2} x^{3} y^{\frac{1}{2}},$ where ‘a’ is a constant. If percentage error in measurement of ‘x’ and ‘y’ are 4% and 12% respectively, then the percentage error for ‘z’ will be…………%

3 Views|Posted a year ago

Asked by Raj Pandey

Answered by

Raj Pandey | Contributor-Level 9

a year ago

$\frac{Δ z}{z} \times 100 = 3 \frac{Δ x}{x} \times 100 + \frac{1}{2} \frac{Δ y}{y} \times 100$

$= 3 \times 4 + \frac{1}{2} \times 12$

$= (12 + 6) %$

$= 18 %$

Upvote

New answer posted•a year ago

Units and Measurement Class 11th

If E, L, M and G denote the quantities an energy, angular momentum, mass and constant of gravitation respectively, then the dimensions of P in the formula P = EL²M^-⁵G^-² are:-

4 Views|Posted a year ago

Asked by Vishal Baghel

Answered by

Vishal Baghel | Contributor-Level 10

a year ago

$P = E L^{2} M^{- 5} G^{- 2}$

$= [M L^{2} T^{- 2}] {[M L^{2} T^{- 1}]}^{2} [M^{- 5}] {[M^{- 1} L^{3} T^{- 2}]}^{- 2}$

$= M^{0} L^{0} T^{0}$

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New answer posted•a year ago

Units and Measurement Class 11th

In a Screw Gauge, fifth division of the circular scale coincides with reference line when the ratched is closed. There are 50 divisions on the circular scale, and the main scale moves by 0.5mm on a complete rotation. For a particular observation the reading on the main scale is 5mm and the 20th division of the circular scale coincides with reference line. Calculate the true reading.

3 Views|Posted a year ago

Asked by Vishal Baghel

Answered by

Vishal Baghel | Contributor-Level 10

a year ago

Pitch = 0.5 mm

Least count = $\frac{p i t c h}{d i v i s i o n} = \frac{0.5 m m}{50} = 0.01 m m$ $\frac{}{} \frac{}{}$

True Reading = 5mm + 20 * 0.01 – 5 * 0.01 = 5.15 mm

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New answer posted•a year ago

Units and Measurement Class 11th

If $Z = \frac{A^{2} B^{3}}{C^{4}},$  then the relative error in Z will be:

2 Views|Posted a year ago

Asked by Vishal Baghel

Answered by

Vishal Baghel | Contributor-Level 10

a year ago

$z = \frac{A^{2} B^{3}}{C^{4}}$

The relative error in z is given by

$\frac{Δ z}{z} = \frac{2 Δ A}{A} + \frac{3 Δ B}{B} + \frac{4 Δ C}{C}$

Upvote

New answer posted•a year ago

Units and Measurement Class 11th

For $z = a^{2} x^{3} y^{\frac{1}{2}},$  where ‘a’ is a constant. If percentage error in measurement of ‘x’ and ‘y’ are 4% and 12% respectively, then the percentage error for ‘z’ will be…………%

5 Views|Posted a year ago

Asked by Alok Kumar Singh

Answered by

Alok Kumar Singh | Contributor-Level 10

a year ago

$\frac{Δ z}{z} \times 100 = 3 \frac{Δ x}{x} \times 100 + \frac{1}{2} \frac{Δ y}{y} \times 100$

$= 3 \times 4 + \frac{1}{2} \times 12$

$= (12 + 6) %$

$= 18 %$

Upvote

New answer posted•a year ago

Units and Measurement Class 11th

Match List I with List II.

List I

List II

A. Torque

I. Nms^-1

B. Stress

II. J kg^-1

C. Latent Heat

III. Nm

D. Power

IV. Nm^-2

Choose the correct answer form the options given below

2 Views|Posted a year ago

Asked by Payal Gupta

Answered by

Payal Gupta | Contributor-Level 10

a year ago

A. Torque $\to_{}^{}$ (iii) Nm

B. Stress $\to_{}^{}$ (iv) Nm^-2

C. Latent Heat $\to$ (ii) J kg^-1

D. Power $\to$ (i) Nm S^-1

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New answer posted•a year ago

Units and Measurement Class 11th

A silver wire has mass $(0.6 \pm 0.006) g, r a d i u s (0.5 \pm 0.005)) m m a n d l e n g t h (4 \pm 0.04) c m .$  The maximum percentage error in the measurement of its density will be:

2 Views|Posted a year ago

Asked by Vishal Baghel

Answered by

Vishal Baghel | Contributor-Level 10

a year ago

Given, m = 0.6 $\pm$ 0.006

$\Rightarrow p = \frac{m}{v} = \frac{m}{π r^{2} l}$

$\frac{Δ ρ}{ρ} \times 100 = \frac{Δ m}{m} \times 100 + 2 \frac{Δ r}{r} \times 100 + \frac{Δ l}{l} \times 100$

= 1 + 2 × 1 + 1

Upvote

List I	List II
A. Torque	I. Nms^-1
B. Stress	II. J kg^-1
C. Latent Heat	III. Nm
D. Power	IV. Nm^-2

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