Physics, 17.01.2020 17:31, gabiii262

Which one of the following equations is dimensionally
homogeneous? show your proof.
a. f = ma
b. f = m(v2/r)
c. f(t2 - t1) = m(v2 – v1)
d. f =mv
e. f = m(v2 – v1)/(t2 – t1)
where
f = force (n)
m = mass (kg)
a = acceleration (m/s2)
v = velocity (m/s)
r = radius (m)
t = time (s)

Answers: 3

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Answers

answered: leigha54

Explanation:

We need to calculate the equations is dimensionally homogeneous.

We know that,

Unit of force is Newton.

1 N = kg-m/s^2

Unit of mass is kg.

Unit of acceleration is m/s².

Unit of velocity is m/s.

Unit of radius is m.

Unit of time is sec.

(a). Given that,

F = ma

Put the unit of all elements

N=kg-m/s^2

Kg-m/s^2=kg-m/s^2

Here, N = kg-m/s^2

This equations is dimensionally homogeneous.

(b). Given that,

$F=\dfrac{mv^2}{r}$

Put the unit in the formula

$N=\dfrac{kg-m^2/s^2}{m}$

kg-m/s^2=kg-m/s^2

This equations is dimensionally homogeneous.

(c). Given that,

$F(t_{2}-t_{1})=m(v_{2}-v_{1})$

Put the unit in the formula

N-sec=kg-m/s

$kg-m/s^2\times sec=kg-m/s$

kg-m/s=kg-m/s

This equations is dimensionally homogeneous.

(d). Given that,

F = mv

Put the unit in the formula

N=kg-m/s

kg-m/s^2=kg-m/s

This equations is not dimensionally homogeneous.

(e). Given that,

$F=\dfrac{m(v_{2}-v_{1})}{t_{2}-t_{1}}$

Put the unit in the formula

$N=\dfrac{kg-m/s}{s}$

kg-m/s^2=kg-m/s^2

This equations is dimensionally homogeneous.

Hence, This is required solution.

answered: Guest

scattering of light by tiny particles in air to produce the colors we see on sky, is dependent on the following factors:

(i) wavelength of light

(ii) size of the scattering particle

(iii) distance traveled by light through the atmosphere.

according to rayleigh's law of scattering, the amount of scattering is inversely proportional to the fourth power of its wavelength. shorter the wavelength, greater is its scattering. hence violet/blue light is scattered more than red.

sun's light is a composite light ( visible light) with wavelengths in the range 400 nm (violet) to 700 nm (red). as sunlight passes through our atmosphere, the molecules of air scatter light according to their wavelengths. during sunrise and sunset, the sun's position is below the horizon. hence light from the sun travels a greater distance in the atmosphere when compared to its position a noon.

as sunlight enters the earth's atmosphere, blue light is scattered away and at the end of its journey in the sky, only red and orange wavelengths remain in the beam.

hence at sunrise and sunset, the sky appears reddish orange.

answered: Guest

electric field is a function of 1/r^2

yes, the force per unit charge for a point charge is inverse square law.