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Properties of X-Ray

To find the d...

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To find the distance d over which a signal canbe seen clearly in foggy conditions, a railwaysengineer uses dimensional analysis andassumes that the distance depends on themass density p of the fog, intensity (power/area) S of the light from the signal and itsfrequency f. The engineer finds that d isproportional to Sn The value of n is

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Q. To find the distance

d

over which a signal can be seen clearly in foggy conditions, a railways engineer uses dimensional analysis and assumes that the distance depends on the mass density

ρ

of the fog, intensity (power / area)

S

of the light from the signal and its frequency

f

. The engineer finds that

d

is proportional to

S

^{1 / n}

n

Q. To find the distance

d

over which a signal can be seen clearly in foggy conditions, a railway's engineer uses dimensional analysis and assumes that the distance depends on the mass density

ρ

of the fog, intensity (power/area)

S

of the light from the signal and it's frequency

f

. The engineer finds that

d

is proportional to

S^{1 / n}

n

I = \frac{P}{4 π r^{2}}

At a large distance

r

from a radio antenna, the intensity of the radio signal

I

is related to the power of the signal

P

by the formula above.

Which of the following expresses the square of the distance from the radio antenna in terms of the

intensity of the radio signal and the power of the signal?

Q. A projectile fired at an angle of

45^{\circ}

travels a total distance

R

, called the range, which depends only on the initial speed

v

and the acceleration of gravity

g

. Using dimensional analysis, find how

R

depends on the speed and on

g

.

\int \frac{d x}{\sqrt{2 a x - x^{2}}} = a^{n} {s i n}^{- 1} [\frac{x - a}{a}]

a =

constant. Using dimensional analysis, the value of

n

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