Question

Assertion- Parallax method is used for measuring distances of nearby stars only.
Reason- With increase of distance from the star, the parallactic angle becomes too small to be measured accurately.
A. Both assertion and reason are correct and reason is the correct explanation for assertion.
B. Both assertion and reason are correct but reason is not the correct explanation for assertion.
C. Assertion is correct but reason is incorrect.
D. Both assertion and reason are incorrect.

Answer 1

Hint: In the given assertion reason type question first we need to check if the given assertion statement is right or wrong. We know that the parallax method is used to find the distance between nearby objects in space. To know if the statement is right or wrong we need to prove it by stating the parallax method. Next we need to consider the reason. We need to if the reason is right or wrong and if it is right, is it the correct explanation for the given assertion statement. Thus we will get the solution.

Formula used:
$\theta =\dfrac{\text{Arc length}}{\text{distance}}$

Complete answer:
We have an assertion reason type question.
Let us consider the two given statements.
The assertion says that the parallax method is used for measuring distances of nearby stars only and the reason statement says that with increase of distance of star, parallactic angle becomes too small to be measured accurately.
Consider two stars at some distance as shown in figure below.

Here ‘$\theta $’ is the angle, ‘$l$’ is the arc length and let ‘D’ be the distance to the object.
In parallax method the equation is given as,
$\theta =\dfrac{\text{Arc length}}{\text{distance}}$
Therefore,
$\theta =\dfrac{l}{D}$
From this we get the distance between the stars as,
$\Rightarrow D=\dfrac{l}{\theta }$
From this equation for distance, we can understand that as the parallax angle increases the distance decreases and as the parallax angle decreases the distances increases.
For a minimum parallax angle, the maximum distance we can obtain is 100 light years.
We know that as the distance between the stars increases the parallax angle will be decreased. And hence we will not be able to measure the angle accurately.
Therefore from this we can say that both the given assertion and reason are correct and also reason is the correct explanation for assertion.

So, the correct answer is “Option A”.

Note:
In an assertion reason type question, we will be given two statements; the assertion and the reason. First we need to check if the assertion statement is correct and later we will check if the reason is correct. If both assertion and reason are correct then we need to check if reason is the correct explanation for assertion. Thus we will get the solution