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Question

2 planets 'Xargonia' and 'Olfuba' have taken keen interest in our star 'The Sun'. They are observing our sun from the observatories built on their planet.

Xargonia is 1 Light year away and the aperture area of its telescope is 1m2, while Olfuba is 2 Light years away and the aperture area of its telescope is 4m2.

Find out whose telescope receives more energy? (Assume the Sun radiates E joules of energy per sec.)


A

Xargonia

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B

Olfuba

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C

Both receive equal

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D

Data insufficient

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Solution

The correct option is C

Both receive equal


So we have to find the energy received by the telescopes.

Okay, no big deal.

What do I know.

The sun radiates E joules of energy per second. The rate at which energy passes through a sphere at 1 light year distance will be… the SAME.

E J/s, right?

The intensity at this sphere will be (power/ area) =E4π(1 light year)2------(1)

Similarly, for Olfuba which is 2 light years away the intensity will be =E4π(2 light year)2------(2)

I hope you remember that a light year is a unit of distance and not time. It’s the distance covered by light in a year.

Now that we know intensity let's find the energy received per unit time at each telescopes.

Intensity =PowerArea

=Power(Area) (Area 2) will give me back my power.

Let’s find the power received by the telescope at Xargonia.

Intensity on sphere at 1 light year =E4π(1 light year)2

Area of Aperture of the telescope = 1m2

So power (energy/time) =E4π(1 light year)2× 1 …(iii)

Similarly

Intensity on sphere at radius 2 light year =E4π(2 light year)2

Area of Aperture of the telescope = 4m2

So power =E4π(2 light year)2× 4=4E4π 4(light year)2 …(iv)

Comparing (3) & (4), they both are equal as you can see

=E4π(1 light year)2

So they both receive equal power.


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