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16 pages/≈4400 words
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Subject:
Biological & Biomedical Sciences
Type:
Exam
Language:
English (U.S.)
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Topic:

Dimensional Formula: Pressure, Power, Kinetic Energy, and Density

Instructions:
In its investigation of gender roles and relationships, "The Tiger's Bride" is more radical and overtly sexual. "The Tiger's Bride" is narrated by the titular bride herself, who starts out by saying, "My father lost me to The Beast playing cards." The idea that women are commodities for barter between men is implied in the story's first statement. This is highlighted further when she claims that her mother likewise died young as a result of her father's gambling, whoring, and excruciating humiliation and was bartered for her dowry to the Russian nobility.
Content:

Solved Example 6

The dimensional formula of the pressure is…..

a) ML2T-2 b) ML-1T-2 c) a or b d) MLT

Steps:

pressure = ForceArea = MLT-2L2

= ML-2T-2

= ML-1T-2

-unit → kg.m-1.s-2= kg./s2= N/m2= N.m-2= J/m3= J.m-3

Solved Example 7

The dimensional formula of the work (energy) is ….

a) ML2T-2 b) MLT-2 c) a or b d) MLT

Steps:

(Energy) Work = Force × displacement

W = F × d

= ML2T-2 × L

= ML2T-2

- unit → kg.m2. s-2 = kg . m2/s2 = Joule = N.m

Note: – Any number has no dimension (as: π ,2,12 ,….)

Solved Example 8

The dimensional formula of kinetic energy is….

a) ML2T-2 b) ML2T-3 c) a or b d) MLT

Steps:

K.E = 12 m v2

= M (LT-1)2

= ML2T-2

- unit → kg.m2. s-2 = kg . m2/s2 = Joule = N.m

Solved Example 9

The dimensional formula of the power is….

a) ML2T-1 b) ML2T-3 c) a or b d) MLT

Steps:

Power = worktime = ML2T-2 T

= ML2T-2T-1

= ML2T-3

- unit → kg.m2. s-3 = kg . m2/s3 = Js = J.s-1 = N.m/s = N.m.s-1

Type equation here.

Solved Example 10

The dimensional formula of the density is….

a) ML2T-1 b) ML-3T0 c) a or b d) MLT

Steps:

Density = MassVolume = mv = ML3 = ML-3

- unit → kg.m-3 = kg /m3

Solved Example 11

The dimensional formula of the linear momentum is….

a) MLT-1 b) ML-3T6 c) a or b d) MLT

Steps:

Linear momentum= mass x velocity

PL = m v

=MLT-1

4162425334010-unit → Kg.m.s-1 = Kg.m/s

20859756985lefttopAndre-Marie AmpereIsaac Newton Kelvin

Solved Example 4

Vf = Vi = [Where Vf : final velocity, Vi : initial velocity, a:acceleration] is the relation?

a- right b- wrong

Steps: Vf= Vi + at

L.H.S= LT-1 R.H.S= LT + LT-2 .T

= LT-1 + LT-1

= 2LT-2

L.H.S=R.H.S

-Relation is right

Remember: -Any number has no dimension

Solved Example 5

From the physical relation: X= C1 + C2 t

( where: X is the distance in meters and t is the time in seconds)

Then the measuring units of the two quantities C1 & C2 are ………………. , ………….

a) m, m/sb) Kg, mc) a or b d) m , s

Steps:

L.H.S = X = L , so→ R.H.S = L

C1 = L = meter

C2t = L

C2 = LT = LT-1 = meter/second

38671508890In the opposite figure, a car moves with velocity ν on a curved path of radius r. If the acceleration of the car is calculated rom the relation; a = rn vm where m and n are numeral constants with no dimensions, then the magnitudes of m and n are ……………………. .

m

n

a)

1

-2

b)

1

-1

c)

2

-2

d)

2

-1

Solution

[a] = [rn vm ]

L T-2 = Ln (LT-1)m = Ln Lm T-m

L T-2 = Ln+m T-m

By comparing the two terminals of the equation : n + m=1

∴N= -1

∴The correct choice is (d)

Integration with mathematics:

You can revise the rules of expone

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