Chapter 13, Problem 1QP

To determine

The correct statement

Answer to Problem 1QP

Option (b)

Explanation of Solution

Write the equation for the brightness of a star.

    $\begin{array}{c}\text{B}=\frac{\text{L}}{4\pi d^2}\\ \text{L}\text{=}\text{B}\times 4\pi d^2\end{array}$        (I)

Here, $B$ is the brightness of the star, $L$ is the luminosity and $d$ is the distance of the star from the earth.

The distance of both the star A and star B is same from the earth. Hence, the luminosity is directly proportional to the brightness. When the brightness of the star A is halved, its luminosity will also become halved. As a result, the star B is now twice as bright as star B.

Conclusion:

Both star A and star B are nearly at same distance from the earth. The brightness of star A being halved does not have any influence on its distance from earth. Therefore option (a) is incorrect.

When the brightness of the star A is halved, its luminosity will also become. As a result, the star B is now twice as bright as star B. Therefore, option (b) is correct.

When the brightness of the star A is halved, its luminosity will also become. As a result, the star B is now twice as bright as star B and does not do anything with the hotness. Therefore, option (c) is incorrect.

The brightness of star A being halved does not anything to do with the size of the star A or star B. Therefore, option (d) is incorrect.