Physics, 02.09.2020 18:01 vanessacox45

The period of a simple pendulum, defined as the time necessary for one complete oscillation, is measured in time units and is given by T=2πlg where l is the length of the pendulum and g is the acceleration due to gravity, in units of length divided by time squared. Show that this equation is dimensionally consistent.

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Answer from: pravikumar01

Explanation:

T = 2π √l/g

The dimension for l = m

The dimension for g = m/s²

The dimension for 2π is nothing. Since it's a constant, it is dimensionless.

Now we proceed ahead. Since we are not using the 2π, for the sake of this proving, our formula will temporarily be written as

T = √l/g

Inputting the dimensions, we have

T = √(m) / (m/s²)

T = √(m * s²/m)

T = √s²

T = s

Since the unit of period itself is in s, we can adjudge that the equation is dimensionally constant.

Answer from: Quest

answer: 802.3 kilo joules of energy represents 191.75 kilo calorie of energy.

explanation:

energy released during combustion of one mole methane = 802.3 kilo joules

if 1 kilo joule = 0.239006 kilo calorie

then ,802.3 kilo joule will be = 802.3 $\times$ 0.239006 kilo calorie

802.3 kilo joule = 191.75 kilo calorie

hence, the energy in kilo calorie is 191.75 kilo calorie.

Answer from: Quest

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.

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